(b)(i) Use Mathematical Induction to prove that for all positive integers n 21 1 1. 1 一 -十 +... 1x3 3x5 5x7 (2n-1)x(2n+1) 2n+1 (ii) Find in simplest fractional form the value of 1 1 ... 11x13 13x15 15x17 119x121

(Proof) For any integer n, n² + n is even.

can you find problems in my homework? can you explain it how you can find the answers?

#6 help!

Please answer parts d-f of this question

The head of a fish measures 22 cm long. The tail is as long as the head and half the body. The body is as long as the head and the tail. How long is the fish?

Suppose a is a positive integer. Simplify the expression a Σ ((n + 2)³ + n³ - 2(n+1)³). n=1 [Explain in words what you are doing at each step. Your answer should not involve a sum, and your method should not involve evaluating a sum.]

n(n + 1) 2 Use the formula S =- 1+2+3+... + 980 = to find the sum of 1 + 2 + 3 + ... + 980.

Discrete Mathematics

Which are you trying to show is true in Step 3 of a proof by mathematical induction for the statement "For all the positive integers, n3+2n is divisible by 3"?     A   n3+2n=k3+2k is divisible by 3     B   n3+2n is divisible by 3     C   k3+2k is divisible by 3   D     (k+1)3+2(k+1) is divisible by 3