For HW 1, Question 1, since any time we have a summation of something in the form 
ix for some constant x that the sum can be calculated using a polynomial where 
the largest term involves nx+1, for this problem, you know the solution will be 
in the form:

    an4 + bn3 + cn2 + dn + e

You need to use constructive induction to solve for a b c d e.
You also might need the base case(s) to help with some of these.