For every integer K from 1-10 inclusive, the kth term of a : PS Archive
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# For every integer K from 1-10 inclusive, the kth term of a

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For every integer K from 1-10 inclusive, the kth term of a [#permalink]

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05 Nov 2006, 13:08
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For every integer K from 1-10 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 & 2
c) between 1/2 & 1
d) between 1/4 & 1/2
e) less than 1/4

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05 Nov 2006, 13:43
Well, the sum of the infinite series is 1/3.

Write out the terms (1/2 - 1/4) + (1/8 - 1/16) + (1/32 - 1/64) +

= 1/4 + 1/16 + 1/64 + ..

which converges to 1/3 very quickly (it's a geometric series).
05 Nov 2006, 13:43
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