设Sn=14+27+.n(3n+1)则Sn=

分类: 作业答案 • 2022-03-12 10:59:39

问题描述：

设Sn=1*4+2*7+.n(3n+1)则Sn=

答

Sn=1*4+2*7+.n(3n+1)
=3*1&sup2+1+3*2&sup2+2+...+3*n&sup2+n
=3*(1&sup2+2&sup2+...+n&sup2)+(1+2+...+n)
=3*n*(n+1)*(2n+1)/6+n*(n+1)/2
=n*(n+1)&sup2

设Sn=1*4+2*7+.n(3n+1)则Sn=