I actually have two questions on the following problem:

It is known that the leading term of the sum \sum_{i=0}^n i is n^2/2, and for the \sum_{i=0}^n i^2 the leading term is n^3/3. Can you make a guess what's the leading term in \sum_{i=0}^n i^3? in \sum_{i=0}^n i^k? Can you prove something inductively for this?

Clearly the guess is the leading term would be: n^{k+1}/{(k+1)}
However, I have two questions here.
1) I don't really understand what this problem means by "leading term". If there are no variables in the sum, how can there be terms?
2) I couldn't find anywhere in my text if an inductive proof applies for just proving a leading term. Does it?

Thank you in advance for your help.