Question

Use mathematical induction to prove the statement is true for all positive integers n.

The integer n3 + 2n is divisible by 3 for every positive integer n.

Answer 1

1] test for n = 1
2] assume true for k = 1

so assumed \(\frac{k^3 + 2k}{3} \in Z\)

3] now see what you can do with \(\frac{(k+1)^3 + 2(k+1)}{3}\), ie with k replaced by k+1

i simply expanded out the numerator and it just came together

Answer 2

thank you