# Proof by induction

by asset101
Tags: induction, proof
 P: 11 Use mathematical induction, to prove that $$\frac{n^{3}+5n}{3}$$ is an even integer for each natural number n. I am fimilar with proof by induction but in most of the question that I have done have a LHS = RHS which seems to simplifiy things a little bit. Any help would be appreciated Cheers 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
HW Helper
P: 1,979
 Quote by asset101 Use mathematical induction, to prove that $$\frac{n^{3}+5n}{3}$$ is an even integer for each natural number n. I am fimilar with proof by induction...
Put n+1 in place of n.

(n+1)^3 + 5(n+1) = n^3+3n^2+3n+1+5n+5 = (n^3+5n) + 3n(n+1) + 6.

Now divide each term by 3 and see what kind of number you get.

Since you are familiar with induction, this should be enough.
 P: 11 Got it thanks mate

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