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For every integer K from 1-10 inclusive, the kth term of a [#permalink]
 05 Nov 2006, 14:08
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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
Answer is d. Please explain.
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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).
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