Maths

posted by .

The first odd number can be expressed as 1 = 1squared - 0squared.

The second odd number can be expressed as 3 = 2squared - 1squared.

The third odd number can be expressed as 5 = 3squared - 2squeared.

a) Express the fourth odd number in this form. (Am I right in saying 7 = 4squared - 3squared)

b) Express the number 19 in this form. (Am I right in saying 19 = 10squared - 9squared)

c) Write down a formula for the Nth odd number and simplify this expression.

d) PROVE that the product of two consecutive odd numbers is always odd.

  • Maths -

    yes, on a,b.
    c) N=((INT N/2)+1)^2-(INT(N/2))^2
    d)Let N be and even number, and M an even number.

    (N+1)(M-1) is the product of two odd numbers
    = NM+M+N-1
    BUt NM is even (the product of two evens), M is even, N is even, so NM+M+N is even. If one subtracted, then the product of two odd numbers is odd.
    If you cannot use the arguement NM is even, then consider
    NM= M+M+M+....M where the M is added N times. The sum of even number is even.
    QED

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Mathematics - Cardinal Number

    Hi, This is a really easy question. I think I am analyzing it too much: Find the cardinal number of the following set: {1,3,5,.....1001} Thanks in advance. Ok, the cardinal number is the numbe of members of a set. The set you've given …
  2. algebra

    I have been working this one for awhile and have become more confused. Please assist. Problem: Find two consecutive odd integers such that 5 times the first interger is 12 more than 3 times the second. The key thing is to realize that …
  3. Statistics

    a roulette wheel has 40 slots evenly divided between red (even) and green (odd) slots totaling 38 and a "0" and a "00". what is the probability of the ball landing in an: A)even number < 10 B) other than an even or odd number C) …
  4. Math

    1. Start with an odd number, e.g. 3. Then the square of 3 can be expressed as the sum of two consecutive numbers, i.e. 32 = 9 = 4 + 5. Therefore the Pythagorean Triples are {3, 4, 5} since 32 + 42 = 52. Generate another set of Pythagorean …
  5. Math

    How to Generate Pythagorean Triples using an Odd Number 1. Start with an odd number, e.g. 3. Then the square of 3 can be expressed as the sum of two consecutive numbers, i.e. 32 = 9 = 4 + 5. Therefore the Pythagorean Triples are {3, …
  6. Math

    A nickel is flipped and a dime is flipped. 1. What is the probability of obtaining exactly one head?
  7. Probability

    A nickel is flipped and a dime is flipped. 1. What is the probability of obtaining exactly one head?
  8. Maths :(

    41 different balls are drawn from a bag containing balls numbered 1,2,…,300. The probability that the number of odd balls drawn is larger than the number of even balls can be expressed as ab where a and b are coprime positive integers. …
  9. maths

    The sum of odd squares can be expressed as 1^2+3^2+5^2+…+(2n-1)^2=An^3+Bn^2+Cn+D. The value of A can be expressed as a/b, where a and b are positive co-prime integers. What is the value of a+b?
  10. Math

    Use the Distributive Property to prove each statement. Hint: you can write an even number as 2n and odd number as 2n + 1, where n represents any whole number. A. The sum of two even numbers is even. B. The sum of two odd numbers is …

More Similar Questions