Gmat数学,求简便算法~~Foreveryintegerkfrom1to10,inclusive,thekthtermofacertainsequenceisgivenby.IfTisthesumofthefirst10termsinthesequence,thenTis(A)greaterthan2(B)between1and2(C)between1/2and1(D)

Question

Gmat数学,求简便算法~~
For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by . 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) between 1/4
the kth term of a certain sequence is given by （-1）^(k+1)乘以(1/2^k)

Answer 1

答案选D,解法如下：
the kth term of a certain sequence is given by （-1）^(k+1)乘以(1/2^k)
说明通项公式为：an=(-1)·（-1/2）^k
又因为K=10,已经是一个较大的数了,1-q^n,在n较大的情况下,是可以忽略的,因此
sn=a1/（1-q）,代入即为:1/2除以1-（-1/2）,答案为1/3.