PP PS 1 Q37

[nemolee]

37.5000-!-item-!-187;#058&004365
For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (-1)^K + 1 (1 / 2^K) . If T is the sum of the first 10 terms in the sequence, then 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

ANS: (D) , 覺得自己是在亂算一通，錯誤的選了(A), 我把 1~10的每一個數字都代入題目的公式，然後得出的每一個答案相加減之後得出 (A)的答案.. ( 好呆的算法)

請問題目是要求出捨摸? 謝謝

PS. 那個式子，怕不清楚，用中文再囉嗦一次：負1的K+1平方後加1 乘上 2的K平方分之1

[FIG]

(-1)^(K + 1) * (1 / 2^K)

我想題目要的問的是
1/2-1/4+1/8......+ 1/512 - 1/1024
所以為D

[nemolee]

感謝