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JeetGulia: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Mon Jun 14, 2010 4:46 am; Thanked: 3 times

Series Problem

by JeetGulia » Sun Sep 12, 2010 3:47 am

For Every integer K from 1 to 10, Inclusive, the Kth Term 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 Corrected

Last edited by JeetGulia on Sun Sep 12, 2010 5:16 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Sun Sep 12, 2010 3:47 am

GMAT/MBA Expert

Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pm; Location: Milpitas, CA; Thanked: 447 times; Followed by:88 members

by Rahul@gurome » Sun Sep 12, 2010 4:48 am

Kth term = (-1)^k+1 * (1/2^k)
1st term = (-1)^1+1 * (1/2^1) = 1/2
2nd term = (-1)^2+1 * (1/2^2) = -1/2^2
So, T = 1/2 - 1/2^2 + 1/2^3 - 1/2^4 +... up to 10 terms
T = (1/2 + 1/2^3 + 1/2^5 + ....) - (1/2^2 + 1/2^4 +....) = (1/2)[1 + 1/2^2 + 1/2^4 + ....] - (1/2^2)[1 + 1/2^2 + 1/2^4 +....]
= (1/2 - 1/4)[1 + 1/2^2 + 1/2^4 + ....] = [1/4][1 + 1/2^2 + 1/2^4 + ....], which implies T > 1/4 and 1 + 1/2^2 + 1/2^4 + .... will always be less than 2.
So, 1/4 < T < 1/2

Please check options (C) and (D), both of them are the same.

Rahul Lakhani
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