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# For every integar K from 1 to 10 inclusive the Kth term of a

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For every integar K from 1 to 10 inclusive the Kth term of a [#permalink]  30 Jan 2006, 18:53
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For every integar K from 1 to 10 inclusive the Kth term of a cetain sequence is given by (-1)^K-1(1/2K). If T is the sum of the 1st 10 terms in the sequence then T is?

>2
b/w 1 & 2
b/w 1/2 & 1
b/w 1/4 & 1/2
<1/4
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1st Term: (-1)^0(1/2) -> 1/2
2nd Term: (-1)^1(1/4) -> -1/4

3rd Term: (-1)^2(1/6) -> 1/6
4th Term: (-1)^3(1/8) -> -1/8

We can see the first part (-1)^k does nothing than to alternate the sign of the outcome. The next part (1/2k) will progressively get smaller as k increases. This will be then subtracted from the previous positive number making that number smaller.

I figure T will be between 1/4 and 1/2 since the smallest base term is 1/4 (1/2-1/4) and adding 10 smaller terms shouldn't make it exceed 1/2
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