1). Prove by induction, for all positive integers n, that:
(1 x 5) + (2 x 6) + (3 x 7) + ..... + n(n + 4) = 1/6 n(n+1)(2n+13)
With induction you assume P(n), and prove p(1) p(n+1)
You prove that this:
1/6 n(n+1)(2n+13) + (n+1)((n+1) + 4)
is equal to this:
1/6 (n+1)((n+1)+1)(2(n+1)+13)
Explanation:
Your given a sequence and told the nth term is "n(n + 4)", and your told the sum of the first n terms is "1/6 n(n+1)(2n+13)". You need to prove that the sum of the first n terms + the (n+1)th term is equal to the sum of the first (n+1) termss.
Hope that helps