The sum of the fourth powers of the first $n$ positive integers I am studying mathematical induction and most of the times I have to prove something. Like, for example:
$1 + 4 + 9 + ...+ n^2 = \frac{n(n+1)(2n+1)}{6}$
This time I found a question that ask me to find a formula for 
$1 + 16 + 81 + .... + n^4$
How can I do this with induction? And is there really a formula for this sum?

I hope this helps :  
http://mathworld.wolfram.com/PowerSum.html
or Faulhaber's formula :
https://en.wikipedia.org/wiki/Faulhaber%27s_formula
