Evaluate the finite sum
T(n)=k=1∑n(3k3+2k2−5k).
Proceed as follows:
(i) Separate T(n) into three individual series and express each in terms of n using standard formulae.
(ii) Simplify your answer from part (i) to obtain T(n) as a single polynomial in n.
(iii) Hence find T(10).