Question

麻烦各位帮我看看这道题第二小题哪里错了 数列求和 错位相减法

Answer 1

错位相减时错了：

1/2Tn=(1/2)^(-1)+2*[(1/2)^0+(1/2)^1+(1/2)^2+...+(1/2)^(n-2)]-(2n-1)*(1/2)^(n-1)

=2+2*[1-(1/2)^(n-1)]/(1-1/2)-(2n-1)*(1/2)^(n-1)

=2+4-4*-4*(1/2)^(n-1)-(2n-1)*(1/2)^(n-1)

=6-(2n+3)*(1/2)^(n-1)

Tn=12-(2n+3)*(1/2)^(n-2)