Question

Find the sum of the series ∑ 4 n = 1 ( 2 n + n 3 )

Answer 1

Step-by-step explanation:

Tn=n(n+1)(n+4)

Tn=n3+5n2+4n

Sn=∑n3+5∑n2+4∑n

=[2n(n+1)]2+85n(n+1)(2n+1)+24n(n+1)

=2n(n+1)[2n2+n+35(2n+1)+4]

=2n(n+1)[63n2+23n+34]

=2n(n+1)(3n2+23n+34).