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?