已知an=5n(n+1)(n+2)(n+3),求数列{an}的前n项和Sn

【方法1：强行展开a(n)表达式】1+2+……+n=n(n+1)/21^2+2^2+……+n^2=n(n+1)(2n+1)/61^3+2^3+……+n^3=n^2(n+1)^2/41^4+2^4+……+n^4=n(15n^3+10n^2-1)/30,然后再代入a(n)=n (n+1)(n+2)(n+3)的展开式中,a(n)展开后是...