Question

If n> 2 , show that n^5 - 5n^3 + 4n is divisible by 120

Answer 1

Answer:

n^5-5n^3 +4n=(n-2)(n-1)(n)(n+1)(n+2)

For n=3,Sn=120

So it is divisible by 120

By finite mathematical induction we can prove Sn divisible by 120