4. Given these formulas: - $i=1?N?1=N$ $-?_{i=1}i=-?_{i=1}i_{2}=??_{i=1}i_{3}=2N(N+1)?6N(N+1)(2N+1)?(2N(N+1)?)_{2}?$ Simplify the expression $i=0?N?1?[N_{4}?32?i_{3}+N_{2}16?i+N2?]$ so as to remove the sigma. Be careful to note the index starting and ending values.

Solution: Given formulas are ?i=1N1=N,?i=1Ni=N(N+1