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Math Help - show integer by induction

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by Anna Maria View Post
    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.
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