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Sum of an infinite series

  1. Apr 14, 2004 #1
    hi, i need a little help calculating the infinite series sorry if it seems confusing, but i dont know how to put in the sigma or intergral symbols i did my best to make it clear:

    i am sopposed to express (integral from 0 to 1) of 2dx/[(3x^4)+16] as a sum of an infinite series heres what i did:

    the (integral from 0 to 1) of 2dx/[(3x^4) + 16]
    i found that the series of 2dx/[(3x^4)+16] = 1/8* (sigma from n=0 to infinity) of (-1)^n *(3x^4/16)^n

    i then pulled out the constants and got

    1/8 * (sigma from n=0 to infinity) (-1)^n * (3/16)^n (integral from 0 to 1) (x^4n)

    after evaluating the integral i got for my infinit series

    1/8 (sigma from n=0 to infinity) (-1)^n (3/16)^n [1^(4n-1)/4n-1]

    i just wanted to know if this seemed like it was the right way.
    thanks
     
  2. jcsd
  3. Apr 14, 2004 #2

    turin

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    Homework Helper

    Yes. I didn't look at the details, but you seem to have the correct approach.
     
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