Hi. I was thinking a bit and I tried to use the definition of differentiation to see how the rules were created like the standard "multiply by the power and minus one from the power" for functions in the form of x^a. That was easy enough.

I then tried to do the same thing with integration using x^a again which should lead me to x^(a+1) / (a+1). I got stuck at a point when testing it with x^2.

Limit n-> Infinity of ( (1 + 2^2 + 3^2 + 4^2 + ... n^2) / n^3 )

How do I solve this limit algebraically?