已知数列{an}中,an=(3n-2)•3的n+1次方,求Sn?
问题描述:
已知数列{an}中,an=(3n-2)•3的n+1次方,求Sn?
答
an = (3n-2).3^(n+1)= 9(n.3^n) -2.3^(n+1)Sn = an+a2+...+an=9[∑(i:1->n)i.3^i ] - 9(3^n-1)letS = 1.3 + 2.3^2 ...+n.3^n (1)3S = 1.3^2+2.3^3+...+n.3^(n+1) (2)(2)-(1)2S =n.3^(n+1) -( 3+3^2+...+3^n)=n.3^(n+...