Math Help - show integer by induction

1. show integer by induction

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

I have tried induction but after expanding the term I get something like 3(k^5)+15(k^4)+35(k^3)+45(k^2)+37k+15.

Any help?

2. Originally Posted by Anna Maria
I have tried induction but after expanding the term I get something like 3(k^5)+15(k^4)+35(k^3)+45(k^2)+37k+15.
What term did you expand?
Induction is a good idea: if you know that $f(n)$ is an integer (where $f(n)$ is your polynomial expression), then expand $f(n+1)-f(n)$. As you will see, what you get is a polynomial with integer coefficients, hence $f(n+1)-f(n)$ is an integer, and since $f(n+1)=f(n) + (f(n+1)-f(n))$ is the sum of two integers, it is an integer.