# proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can

38,458 results
1. ## mathematics

The spinner is divided into 6 equal parts. If it is spun twice, find the probability that a. Both spins stop on even numbers b. Both spins stop on odd numbers. c. One is odd and the other is even d. The sum on the first spin and second spin is less than or

2. ## Math

The sum of 3 consecutive odd natural numbers is 69. Find the prime number out of these numbers.

3. ## algebra

Are the following true or false? 1. The difference of two natural numbers is always a natural number. 2. The sum of two natural numbers is always a natural number. 3. The quotient of two natural numbers is always a natural number. 4. The difference of two

4. ## Algebra

Choose which group of sets the following number belongs to. Be sure to account for ALL sets. 2/5 A. Real numbers, rational numbers. B. Real numbers, irrational numbers. C. Rational numbers, natural numbers, integers. D. Irrational numbers, natural numbers.

5. ## maths geometry

the sum of three consecutive odd natural number is 153 find the numbers

6. ## Math

(1, 1, 8) is a triple of natural numbers which has a sum of 10. Consider (1, 8, 1) and (8, 1, 1) to be the same triple as (1, 1, 8). How many different triples of natural numbers have a sum of 10? Include (1, 1, 8) as one of your triples.

7. ## precalculus

Can you please check my answers? 1.Find Pk + 1 if Pk=2^K-1/k! answer: 2^k+1/(k+1)! 2.Find Pk + 1 if Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) answer: 7+13+9...(6k-1+1)+6k+1 +(6k+2) 3.What is the first step when writing a proof using mathematical

8. ## math

The sum of two numbers is equal to 495. The last digit of one of them is zero. If you cross the zero off the first number you will get the second. What are the numbers?

9. ## Maths

Find three consecutive natural numbers such that the sum of the first and the second is 39 more than the third number.

10. ## Math

1. If the product of 5 and the sum of 10 and a certain number is equal to 15, what is the number? 2. The sum of two consecutive counting numbers divided by their positive difference is 9. Find the larger numbers.

11. ## Math

question 1: A series is: 1. any list of numbers 2. a summation of quantities whose positions are based upon the natural numbers 3. an arrangement of quantities whose positions are based upon the natural numbers. Which number is it? question 2: For the rule

12. ## Algebra

Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.

13. ## College Algebra

The sum of three consecutive natural numbers is 966. Find the numbers.

14. ## Math. NEED HELP ASAP.

Im very confused on this. List all the numbers from the given set that are: a. Natural numbers, b. Whole numbers, c. Integers, d. Rational numbers, e. Irrational numbers, f. Real numbers. {-3, -2/5, 0, 0.3, ✓3, 5.8, ✓100} list all the natural numbers

15. ## computer sciece(Computation Theory)

Find the error in the following proof that all horses are the same color. CLAIM: In any set of h horses, all horses are the same color. PROOF: By induction on h. Basis: For h = 1. In any set containing just one horse, all horses clearly are the same color.

16. ## Mathematical Induction

Use mathematical induction to prove that the following is true. 8+11+14...+(3n+5)=1/2n(3n+13), for all n in the set of natural numbers.

17. ## Math

The sum of three consecutive natural number is 153.find the numbers

18. ## math induction

prove the product of 4 consecutive integers is always divisible by 24 using the principles of math induction. Could anyone help me on this one? Thanks in advance! Sure For induction we want to prove some statement P for all the integers. We need: P(1) to

19. ## precalculus

Find Pk + 1 if Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) 7 + 13 + 19 + …+[6(k - 1) + 1] + (6k + 1) + [6(k + 1) + 1] 8 + 14 + 20 + …+[7(k - 1) + 1] + (7k + 1) 7 + 13 + 19 + …+(6k + 1) 7 + 13 + 19 + ...+[6(k - 1) + 1] + (6k7 +1) + (6k + 2)

20. ## INTERMEDIATE ALGEBRA

HOW DO I FIND OUT WHAT The sum of three consecutive natural numbers is 870, find the numbers

21. ## mathematics

the sum of two numbers is 31. 2/3 of one of the numbers added is equal to 5/8 of the other.find the two numbers

22. ## college algebra

The sum of three consecutive natural numbers is 651, find the numbers. 3*7*31 21*31=651 is what I put for my answer but that was incorrect on the homework. Please help me Another Question I had problems with was :Your weekly paycheck is 25 percent less

23. ## Math

1.(A)(i)Show that 2+4+6+8+..+2n=n(n+1). (ii)Find the sum of the first 200 even numbers. (iii)Find the sum of the first 200 odd numbers. (B)(i)Use the formula at the beginning of the question to find the sum of the first 2n natural numbers. (ii)Find a

24. ## discrete math

1)prove that if x is rational and x not equal to 0, then 1/x is rational. 2) prove that there is a positive integers that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive? For 1) use the definition of

25. ## algebra

2.Which of the following is an example of closure. a. The equation 4−6=−2 is an example of the whole numbers being closed under subtraction. b. The equation 1.5+1.6=3.1 is an example of the rational numbers being closed under addition. c. The equation

26. ## lgebra

The sum of three consecutive natural numbers is 963, find the numbers. (A) First, write out an equation that models the relationship between these three numbers: x + ____ +______ = 963 2nd number 3rd number (B) Now, simplify the left side of your equation:

27. ## MATHS

Please Help Me The Sum Of Two Square Of Two Consecutive Natural Number Is 313. Find The Numbers.

28. ## precalculus

how to prove that this is true for all natural numbers n, using principle of mathematical induction. (3i+2)= 5+8+11+14+...+ (3n+2)=3n^2+7n/2

29. ## Permutation and combination

How many natural numbers are there with the property that they can be expressed as sum of cubes of two natural numbers in two different ways.

30. ## MATH

A set of numbers has “the triple-sum property” (or TSP) if there exist three numbers in the set whose sum is also in the set. [Repetitions are allowed.] For example, the set U = {2, 3, 7} has TSP since 2 + 2 + 3 = 7, while V = {2, 3, 10} fails to have

31. ## Algebra

3 real numbers that form a geometric progression have sum equal to 175 and product equal to 17576. What is the sum of the largest and smallest numbers?

32. ## Stat 214

Three identical chips, each with 0 on one side and 1 on the other, are to be tossed simultaneously. A. writes the sample space. B. what is the probability of observing the sum of the face-up numbers to equal to 2? C. What is the probability of observing

33. ## Computer proof

Prove by induction on all positive integer k that if m is any ordinary nfa with k states, and m has fewer than k - 1 transitions, then there exists a state of m that is not reachable. Let N be the λ-NFA: "L" for "λ" b >(1) -----> ((2)) | ^. | b| | L. | a

34. ## Math

Fifteen numbers are written on the circle. Each number is equal to the absolute value of the difference of the next two numbers (moving clockwise). Find the greatest of the numbers, if sum of all numbers is 2.

35. ## math

List the following subsets of the real numbers in order from least inclusive to most inclusive.(1 point) rational numbers, natural numbers, whole numbers, integers whole numbers, natural numbers, integers, rational numbers natural numbers, whole numbers,

36. ## Integers

Suppose a1, a2, . . . , an is a list of n numbers with the following properties: The sum of those n numbers is 500. The sum of the smallest three of those numbers is 48. The sum of the largest two of those numbers is 35. (Note: There might be some

37. ## math

The sum of two numbers is equal to 63 and their difference is equal to 12. Find the numbers.

38. ## Grade 8 Math

Can you write them in Mathematical/numbers form I'll solve them myself. i don't really get it though i have written the first one in mathematical for but i'm not sure if that's right. 1. When six is subtracted from five times a certain number, the result

39. ## proof by induction

proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.

40. ## Math - PreCalc (12th Grade)

If Sn represents the sum of the squares of the first n natural numbers, use proof by induction to find which of the following expressions for Sn is true? A) Sn = n(n − 1)/3 B) Sn = n(2n − 1)/3 C) Sn = n(n + 1)/3 D) Sn = n(n + 1)(2n + 1)/3

41. ## pre calc

If Sn represents the sum of the squares of the first n natural numbers, use proof by induction to find which of the following expressions for Sn is true? Sn=n(n-1)/(3) Sn=n(2n-1)/(3) Sn=n(n+1)/(3) Sn=n(n+1)(2n+1)/(3)

42. ## Algebra ASAP

so this is a fill in on a worksheet and I am having difficulty as the ones I inserted are incorrect can anybody help me how to do it all, sorry it's a long problem. Show that 3^2n − 1 is divisible by 8 for all natural numbers n. Let P(n) denote the

43. ## math

The sum of the first 5 natural numbers is 15 or (5)(6)/2. The sum of the first 21 natural numbers is 231=(21)(22)/2, and the sum of the first 30 numbers is 465. Use inductive reasoning to derive the formula for the sum of the first n natural numbers.

44. ## Discreet Mathematical Structures

Use proof by contraposition to prove the following statement: If A is the average of two positive real numbers then one of the two numbers is greater than or equal to A. Proof. Domain: positive real numbers P: A=(x+y)/2 Q: x is greater than or equal to A

45. ## math

Consider an equilateral triangle with points located at each vertex and at each midpoint of a side. (See picture.) This problem uses the set of numbers {1, 2, 3, 4, 5, 6}. Place one number at each point. Call the sum of the three numbers along any one side

46. ## mathematics

If r and s are natural numbers, then 1/2 (r+s)≥√rs. How can I proof it using direct proof? Thank you.

47. ## math

Write two mixed numbers so that all rules are applied: 1. One number is larger than the other by 4 2/3 2. The difference of the numbers is equal to the smaller number. 3. The sum of the numbers is natural number. What are the numbers?

48. ## discrete math

Could someone help me with this induction proof. I know its true. given then any integer m is less than or equal to 2, is it possible to find a sequence of m-1 consecutive positive integers none of which is prime? explain any help is greatly appreciated

49. ## Induction

Given the series 1,2,3,4,5,10,20,40,80,..... which starts as an arithmetic series for the first five terms and then follows geometric series. It can be proved by strong induction that any positive integer can be written as a sum of distinct numbers of this

50. ## Math - Algebra I

Consider the subsets of R defined as follows: An is the interval (0,1/n) for all natural numbers. Show that: U (union) n=1 to infinity of An = (0,1) Here's what I tried as a proof: Show that (0,1) is a subset of U n=1 to infinity An Take an arbitrary real

51. ## Urgent math

I eliminated 2 of the 5 and now I have 3 I am confused towards which is the right one? help mathematical induction to determine which formula is true for all natural numbers n ≥ 3 a) 2n2 > (n + 1)2 b) (n − 1)2 > n2 − 6 c) (n + 1)2 < n2 +

52. ## Michael

How many natural numbers are there with the property that they can be expressed as sum of cubes of two natural numbers in two different ways.

53. ## Math

Use induction to prove the sum of the first n odd numbers, or 1 + 2 + 3 +....+ (2n 1) = n^2

54. ## Algebra

3 real numbers that form a geometric progression have sum equal to 175 and product equal to 17576. What is the sum of the largest and smallest numbers?

55. ## Discrete Math

Could someone help me with this induction proof. I know its true. given then any integer m is greater than or equal to 2, is it possible to find a sequence of m-1 consecutive positive integers none of which is prime? explain any help is greatly appreciated

56. ## Math

(1, 1, 8) is a triple of natural numbers which has a sum of 10. Consider (1, 8, 1) and (8, 1, 1) to be the same triple as (1, 1, 8). How many different triples of natural numbers have a sum of 10? Include (1, 1, 8) as one of your triples. Is there a fast

57. ## Geometric progression

sum of 4 terms of g p is 30 & sum of first and last term is 18 . Find gp a(r^4-1)/(r-1) = 30 a + ar^3 = 18 a(1+r^3) = 18 it's easy to see that if a=2, r=2 Does that work on S4? 2*15/1 = 30. Yes So, the GP is 2,4,8,16,... But sir I want not logic proof ,

58. ## science,technology and the environment

describe,compare and contrast induction and deduction as methods of science.using examples where appropriate.Identify and solve a problem using both induction and deduction.where appropriate illustrate why and how one would use experimentation and cycle of

59. ## Math! Please check!

Consider the statement: If two whole numbers are even, then their sum is odd. What assumption should be made to prove the statement indirectly? A- The numbers are equal. B- The numbers are not equal. C- Their sum is not odd. D- Their difference is even. My

60. ## Science ...Urgent plz

Describe, compare and contrast INDUCTION and DEDUCTION as methods of science – using examples where appropriate. Identity and solve a problem using both induction and deduction. Where appropriate illustrated why and how one would use experimentation/

61. ## math

Prove that at least one of the real numbers A1, A2, …, A(n) is greater than or equal to the average of these numbers. What kind of proof did you use?

62. ## Stat 214

Three identical chips, each with 0 on one side and 1 on the other, are to be tossed simultaneously. A. writes the sample space. B. what is the probability of observing the sum of the face-up numbers to equal to 2? C. What is the probability of observing

63. ## sir steve reiny plz maths

Suppose you have 5 real numbers whose sum of squares is equal to 5. What is the maximum value of the sum of cubes of these 5 numbers? Please show step

64. ## pre-calculus

Prove 3+4+5+...+(n+2) = [n(n+5)]/2 for n>4 Do the first step in a proof by induction.

65. ## precalculus

How would you describe a proof by mathematical induction?

66. ## MATh Methods

1. The cost of producing x hundred litres of olive oil is 20 + 5x dollars. If the revenue from the sale of x hundred litres of the oil is 1.5x2 dollars, calculate to the nearest litre, the number of litres that must be sold to make a profit of \$800. 2. The

67. ## Maths

If the sum of two natural numbers is 77 and its gusa 7, then all the pairs of searches will be done How to write the sum?Steps send plz

68. ## Math

Can someone please help me write this statement out in formula form. There should be two formulas. Question.... Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the numbers. If we let X = larger

69. ## Math/ Number sense

Use the numbers shown. Make the sum of the numbers across equal the sum of the number down. 7 5 1 9 3

70. ## Math

Most natural numbers can be expressed as a sum of two or ore consecutive positive intergers. Find all natural numbers between 1,000 and 10,000 which cannot be expressed as a sum of tow or more consecutive positive intergers.

71. ## mathematics

Question # 1: A series is: 1. any list of numbers 2. a summation of quantities whose positions are based upon the natural numbers 3. an arrangement of quantities whose positions are based upon the natural numbers. Which number is it? Question # 2: For the

72. ## Math

Can someone check my answers and help me 1. A vector in standard position has its initial points at (0,0) True? 2. The general formula for finding the probability of two events A and B that are not mutually exclusive and overlap is given by: P(A or B) =

73. ## Math

What is 2 + 2? = 4 What is 2 * 2? = 4 So, the sum and the product of these two numbers is the same. Are there other numbers that have this same property? Yes Determine all number pairs x and y such that the product of x and y and the sum of x and y are

74. ## Math

four times the difference or two posotive integer numbers is equal to half the sum of the numbers. If one of the numbers is 14, what is the other number? I just cant get this can anyone help me?

75. ## Pre-Calculus

What makes a mathematical induction true? I know how to solve both steps in the proof, but how do you reach this conclusion?

76. ## can you check my answers precalculus

can you check my answers? Find Pk + 1 if Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) 7 + 13 + 19 + …+[6(k - 1) + 1] + (6k + 1) + [6(k + 1) + 1] 8 + 14 + 20 + …+[7(k - 1) + 1] + (7k + 1) 7 + 13 + 19 + …+(6k + 1) 7 + 13 + 19 + ...+[6(k - 1) + 1] +

77. ## precalculus

can you check my answers? Find Pk + 1 if Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) 7 + 13 + 19 + …+[6(k - 1) + 1] + (6k + 1) + [6(k + 1) + 1] 8 + 14 + 20 + …+[7(k - 1) + 1] + (7k + 1) 7 + 13 + 19 + …+(6k + 1) 7 + 13 + 19 + ...+[6(k - 1) + 1] +

78. ## Math

Encircle the error in the following "proof" that the two arbitrary numbers are equal to each other. Let a and b the arbitrary numbers such that a is not equal to b. Then, (a - b)^2 = a^2 - 2ab + b^2 = b^2 - 2ab + a^2 (a - b)^2 = (b - a)^2 a - b = b - a 2a

79. ## maths

Find all possible pairs of two natural numbers whose sum is 77 and their g.c.d. is 7

80. ## maths

Find all possible pairs of two natural numbers whose sum is 77 and their g.c.d. is 7

81. ## maths

Find all possible pairs of two natural numbers whose sum is 77 and their g.c.d. is 7

82. ## maths

Find all possible pairs of two natural numbers whose sum is 77 and their g.c.f is 7

83. ## math question

-The product of all the positive factors of 20 ( including 20) can be written2^x.5^y. Find x+y. -The number 18 is equal to 2 times the sum of its digits: 1+8=9. 2x9=18. There are 4 two digit numbers that are equal to 4 times the sum of their digitss . Find

84. ## C programming

Enter two integers between 1 to 10 3 4 Both numbers are less than 5. The sum of two numbers is:-1081825676 The product of two numbers is:-1081825680 why are the sum and product so weird? my code: #include int main() { int x; int y; int z; int p; int

85. ## math

For each number, circle the subset(s) of the real numbers that the number belong to. 26) √49 rational, integers, whole numbers, natural numbers, irrational 27) −√81 rational, integers, whole numbers, natural numbers, irrational 28) √43 rational,

86. ## Math

"The conjugate of the sum of two complex numbers is equal to the sum of the conjugates of the two complex numbers." This is true right?

87. ## math

what is the sum of the two least natural numbers that each have exactly six distinct,positive factors?

88. ## Mathematics Probability

S = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} is a set of 10 natural numbers. Suppose, 6 numbers are chosen from the set at random. What is the probability that equal number of even and odd numbers are chosen?

89. ## Algebra

Ursula wrote the sum 5.815 +6.021 as a sum of two mixed numbers. part A. What sum did she write? b. Compare the sum of the mixed numbers to the sum of the decimals? Please answer both questions thanks

90. ## math

Make the sum of the numbers across equal the sum of the numbers down. 7 5 1 9 3

91. ## Math

What numbers can be expressed as an alternating-sum of an increasing sequence of powers of 2 ? To form such a sum, choose a subset of the sequence 1, 2, 4, 8, 16, 32, 64, . . . (these are the powers of 2). List the numbers in that subset in increasing

92. ## Algebra- please help answer

Ursula wrote the sum of 5.815 plus 6.021 as a sum of two mixed numbers? A. What sum did she write? B. Compare the sum of the mixed numbers to the sum of the decimals? Please help answer ASAP. Thanks

93. ## math word problem

can someone help me solve this? not just an answer but a method of solving cause im having a hard time grasping this. Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the numbers.

94. ## Math riddle

nine odd numbers have a sum of 243.find the sum of the first and last numbers in a set of numbers. hint:if three numbers when added equals twelve then represent it by adding n+()n+1. no one cares...durrr....

95. ## Math riddle

nine odd numbers have a sum of 243.find the sum of the first and last numbers in a set of numbers. hint:if three numbers when added equals twelve then represent it by adding n+()n+1.

96. ## math(A.P)

the least vaue of 'n' for which the sum of the first n-odd natural numbers exceeds 5000 is?

97. ## Maths

The product of two natural numbers is 18. If one is added to four times the smaller number this is equal to the larger number. Find both numbers

98. ## Math

Out of the numbers divisible by 3, we picked 4 consecutive numbers. To the sum of these, we added a third of the sum, and then the half of the third of the sum. We got 225. What are those 4 numbers?

99. ## maths

find the sum of all two digit natural numbers which when divided by 7 yield 1 as remainder..

100. ## Maths

What are 3 5-digit numbers that have the sum of their digits equal? Is it as simple as finding a random 5 digit number than switching the number order and making 2 new numbers with the same digit sum? thank you