Question

已知一个数例的通项公式：an=10*n^2+20*n+10(n>=1),求此数例的前n项和Sn!

Answer 1

Sn=∑an=∑(10n^2+20n+10)=10∑n^2+20∑n+10∑1

=10*1/6*n(n+1)(2n+1)+20*n(n+1)/2+10n

5(2n^3+3n^2+n)/3+10(n^2+n)+10n

=5/3*(2n^3+9n^2+13n)

已知Sn,求n,只能解方程了.