Question

Use mathematical induction to prove the statement is true for all positive integers n.
The integer n^3 + 2n is divisible by 3 for every positive integer n.

Answer 1

So far I have:
For n = 1
1^3 + 2(1) / 3 = 3/3 = 1
True

For n = k
k^3 + 2k / 3

n = k + 1
(k+ 1)^3 + 2(k +1) / 3

Answer 2

just plough on with it. you have

\(\dfrac{ (k+ 1)^3 + 2(k +1) }{ 3}\)

\(= \dfrac{ k^3 + 3k^2 + 3k + 1 + 2(k +1) }{ 3}\)

\(= \dfrac{k^3 + 2k}{3} + \dfrac{3k^2 + 3k + 3}{3}\)

can you se where this is going?!?! just needs finishing off