sequence problem

[tanyatomar]

for every integer k from1 to 10 inclusive, the kth term of certain sequence is given by [(-1)^(k+1)].(1/(2^k)). If T is the sum of 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 1/2 and 1/4

e) less than 1/4

OA: d

please explain how to sove this kind of problems fast.. i made mistake of selecting c in hurry ...

[LazyNK]

Hi Tanya,
I find some questions aswell which I am unable to solve in 2 minutes. Buffer generated from some questions which I would have completed in less than 2 minutes helps there. This question could also be one of those, as by the time you have read and reformulated the question, it could be about a minute, or even a minute and half. Don't know how you solved it, but the best way to solve this as per me is to observe following :

nth term=(-1)^(k+1)/2^k= -(-1/2)^k
Every odd term is positive and even term is negative
Also this is a reducing sequence, so if I pair consecutive odds and evens, the odd term will be greater than even term. Also, if I pair consecutive even and odd terms, the even term will be greater than the odd term.

Sum= [1/2-1/4] + [1/8-1/16] +... [(1/2)^9-(1/2)^10] ( pairing of consecutive odd and even terms)
= [1/4] + positive number > 1/4 ---1
Also, Sum= [1/2] - [1/4-1/8] - [1/16-1/32] -... -[(1/2)^8-(1/2)^9] - (1/2)^10 (pairing even and odd terms)
= 1/2 - negative number < 1/2 ---2

Inequations 1 and 2 imply that the sum will be between 1/4 & 1/2, so d.

-NK

[RonPurewal]

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