homework help > math > calculus q&a board > topic: find the sum of the series?...

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posted by  nicky2588 on 8/19/2009 9:22:10 AM  |  status: Closed  |  Earned Karma: 25

Find the sum of the series?

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Question Details:
8-4+2-1+1/2-1/4+1/8-1/16+........
nicky
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Sage
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posted by babumoshai on 8/19/2009 9:46:46 AM  |  status: Live
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Response Details:
8-4+2-1+1/2-1/4+1/8-1/16+........
= 5 - f
where f is the infinite series
f = -1/2+1/4-1/8+1/16- ......
= sum(n from 1 to infinity)[(-1)^n/(2n)]
= - (1/2) ln(2)
answer = 5+(1/2)ln(2) = 5.3466
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posted by velixy on 8/19/2009 9:47:35 AM  |  status: Live
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Response Details:
8-4+2-1+1/2-1/4+1/8-1/16+........

Sum[(-1)^(n)*8/2^(n),{n,0,∞}]  = 16/3  =  5.33333
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posted by Kingle on 8/19/2009 9:57:51 AM  |  status: Live
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Response Details:
let    multiply through by -1

so

so  

we see that we have an alternating geometric series





  multiply through by -1

      where a = 1  and r = -1/2

we know that a geometric series of the form   if

since   then we have

     ====>       ====>       ====>  

    ====>      ====>

therefore since




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