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Math Help - inverse trig and geometric series

  1. #1
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    inverse trig and geometric series

    I learned about series recently. I noticed a slight similarity between a geometric series \sum_{n=0}^{\infty} ar^{n} = \frac{a}{1-r}; |r| < 1

    and a integral, say \int_{a}^{b} \frac{1}{1-x^2}dx

    can you solve using a series instead of trig sub?
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  2. #2
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    Re: inverse trig and geometric series

    u can use the fact that 1/(1-x)=1+x+x^2+x^3+..
    so 1/(1-x^2)=1+x^2+x^4+...
    now if u have read truncation rule
    u can take first three terms only and rest can be assigned as O(x^n)
    this would give u the approximated result
    Thanks from Jonroberts74
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