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# sum of terms

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VP
Joined: 18 May 2008
Posts: 1258

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29 Jan 2009, 04:40
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Kudos [?]: 527 [0], given: 0

SVP
Joined: 17 Jun 2008
Posts: 1534

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29 Jan 2009, 05:27
It should be between 1/4 and 1/2.

Sum of terms will be 1/2 - 1/2^2 + 1/2^3 ......- 1/2^10
=1/2^2 + 1/2^4 + ....+ 1/2^10
using GP series formula,
= 1/3 (1 - 1/2^10) and is very close to 1/3.

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SVP
Joined: 07 Nov 2007
Posts: 1792

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Location: New York

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29 Jan 2009, 09:15
if you forget or don't know GP series..
=1/2 - 1/2^2 + 1/2^3 ......- 1/2^10
= (1/2+1/2^3+..1/2^9)- 1/2*(1/2+1/2^3+..1/2^9)
= 1/2* (1/2+1/2^3+..1/2^9)
clearly above calculation >1/4 and <1/2

D
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Kudos [?]: 1062 [0], given: 5

Re: sum of terms   [#permalink] 29 Jan 2009, 09:15
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