Induction Proof Help: Showing (n^5)/5 + (n^3)/3 + 7n/15 is Integer

[Anna Maria]

I need to show that (n^5)/5 + (n^3)/3 + 7n/15 is an integer for all n.


I tried induction that obviously work for 1 but i could not manage to show this for k+1. Any tips please?

 

[rmcdra]

try expanding the k+1 case. Pascals triangle is a huge help for figuring out how to expand it. After expanding and factoring, you should see the base case and your hypothesis.