在等比数列{an}中,Sn为{an}的前n项和,且S3=
(1)求an. (2)求数列{nan}的前n项和Tn. |
(1)当q=1时,不合题意,舍去-------------------------(1分)
当q≠1时,
=a1(1-q3) 1-q
且7 2
=a1(1-q6) 1-q
,63 2
解得q=2,a1=
---------------------------------------(4分)1 2
所以an=2n-2------------------------------------(6分)
(2)nan=n•2n-2---------------------------------------------------(7分)
所以Tn=1•2-1+2•20+3•21+…+n•2n-2①
2Tn=1•20+2•21+…+(n-1)•2n-2+n•2n-1②
①-②:-Tn=
+20+21+…+2n-2-n•2n-1--------------------------(9分)1 2
所以Tn=(n-1)•2n-1+
----------------------------------------------------------(12分)1 2