讨教书学-PP珀杰般的PP-PS1-完整详解中37题

chloeyeah21

请问PP珀杰般的PP-PS1-完整详解中37题（12页）的题怎么解？
From every integer k from 1 to 10, incluseive the kth term of a certain sequenc is given by (-1)^(k+1) * 1/2^k, If T is the sum of the first 10 terms in the sequce, the T is
A greater than 2
B between 1 and 2
C between 1/2 and 1
D between 1/4 and 1/2
E less than 1/4
请问为什么答案为 D？

sdcar2010

k=1; 1/2
k=2; -1/4
k=3; 1/8
k=4; -1/16
.
.
k=9; 1/(2^9)
k=10; -1/(2^10)

T = (1/2 + 1/(2^3) + .. +1/(2^9)) - (1/(2^2) + 1/(2^4) .. + 1/(2^10))
= (1/(2^2) + 1/(2^4) .. + 1/(2^10))