Yipeeee!
This is a two step process.
1) show that by subbing in n=1 that the answer is a multiple of 3
2) assume true for n=k and show true for n= k + 1
n(n+1)(n+5)is a multiple of 3 proove it by mathematical induction.
2 answers
n(n^2 + 6 n + 5)
n^3 + 6 n^2 + 5 n
if n = 3 k where k is any old integer
27 k^3 + 54 k^2 + 15 k
= 3 (9 k^3 + 18 k^2 + 5 k)
n^3 + 6 n^2 + 5 n
if n = 3 k where k is any old integer
27 k^3 + 54 k^2 + 15 k
= 3 (9 k^3 + 18 k^2 + 5 k)