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 formula, in its simplest form, for 1+3+5+7+9+...+(2n-1)

asked by arzam
  1. using induction
    if n=1, 2 = 1(2) = 2

    assuming true for n=k,
    check for n=k+1:
    2+...+2k+2k+2
    = k(k+1) + 2k+2
    = k(k+1) + 2(k+1)
    = (k+1)(k+2)
    as desired.

    1+3+5+...+(2n-1) = n^2

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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
  2. arithmetic

    1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term
  3. arithmetic

    1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term
  4. SUMS?

    what is the sum of the first towo odd numbers? what s the sum of the first three odd numbers? what is the sum of the first 4,5 and 25 odd numbers? what is the sum of any number (n) of odd numbers? explain your reasoning. IM SORRY
  5. 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.
  6. 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....
  7. Math 8th grade

    I NEED THESE IN ALGEBRAIC EXPRESSION!! The larger of two sums is 12 more than the smaller. Their sum is 84.Find the numbers. The sum of two numbers is 45. The first is 9 less than the second.Find the numbers. The second of two
  8. Geometry

    CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers.
  9. Math

    What is the sum of the first 200 odd numbers? A rectangle has an area of 120 cm square we are trying to find possible perimeters. It's length and width are whole numbers. What are all the possibilities for the 2 numbers? Give next
  10. 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

More Similar Questions