18题

问题描述:

18题
已知数列{an}的前n项和为Sn=n的平方n
1.球数列{an}的通项公式
2.若bn=(1/2)的an次方+n,球数列{bn}的前n项和Tn

1)
A(n) = S(n) - S(n-1) (n≥2)
= n^2 - (n-1)^2
= 2n - 1
当n = 1时,A(1) = S(1) = 1
所以: A(n) = 2n - 1 (n∈N*)
2)
T(n) = b(1) + b(2) + …… + b(n)
= (1/2) + (1/2)^3 + (1/2)^5 + …… + (1/2)^(2n-1)
= (1/2)[ 1 - (1/4)^n ]/( 1 - 1/4 )
=2/3 - (2/3)*(1/4)^n
T(n) = 2/3 - (2/3)*(1/4)^n(n∈N*)