Maths

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.

  1. 👍
  2. 👎
  3. 👁
  1. 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

    1. 👍
    2. 👎
    👤
    bobpursley

Respond to this Question

First Name

Your Response

Similar Questions

  1. Geometry

    Working on conjectures. The question is Conjecure: The product of any two odd numbers is _____? It shows several examples of odd numbers x odd numbers and the products are all odd. So I think the right answer is "odd numbers" but

  2. Math

    A two-digit locker combination is made up of two non-zero digits. Digits in a combination are not repeated and range from 3 through 8. Event A = choosing an odd number for the first digit Event B = choosing an odd number for the

  3. math

    which expression represent the product of 2 consecutive odd integers where n is an odd integer? 1)n(n+1) 2)n(n+2) 3)n(n+3) 4)2n+1

  4. Math

    We call a natural number "odd looking" if all its digits are odd.How many 4-digit odd looking numbers are there?

  1. Math:Probability

    A locker combination consists of two nonzero digits, and each combination consists of different digits. Event A is defined as choosing an odd number as the first digit, and event B is defined as choosing an odd number as the

  2. help me plz

    if a and b are both odd integers, which expression must always equal an odd integer? 1 a+b 2 a*b 3 a-b 4 a/b

  3. discrete math

    use a direct proof to show that the product of two odd numbers is odd. Proofs: (all the nos. i used are odd) 3 x 3 = 9 5 x 9 = 45 7 x 3 = 21 Yes, but you didn't prove the statement for "all" odd integers, only the odd integers you

  4. math

    Which characteristic is correct for the function f(x)=−2x3+3x ? neither even nor odd even both even and odd odd

  1. Calculus, check my answers, please? :)

    Okay, so I think these are right, but I would appreciate if someone could check them and tell me if something is wrong and what the right answer is. I'd also appreciate an explanation if possible. :)Thank you! 7. Given that

  2. math

    Nine cards are numbered 1-9. what is the probability of drawing a number greater than 6 or an odd number. I know the answer is 2/3 but I don't know how you find the probability when it says "greather than 6 OR and odd number"...

  3. Calculus, check my answer, please! 2

    Consider the following functions: f(x)=sin(x^4-x^2) h(x)=(|x|-3)^3 g(x)=1n(|x|)+3 s(x)=sin^3(x) Which of the following is true? h and g are even, f and s are odd. f is even, h and s are odd. h and s are even, f is odd. ***f and h

  4. Math Proof

    Prove that square root of 12 is irrational. **I don't know if I did this correctly PF: By contrapositive, assume sqrt(12) is rational. Then there exist an a,b as integers such that a/b is written in the lowest terms, and

You can view more similar questions or ask a new question.