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Find the sum sum(r =1)^(oo) tan^(-1) ((2...

Find the sum `sum_(r =1)^(oo) tan^(-1) ((2(2r -1))/(4 + r^(2) (r^(2) -2r + 1)))`

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AI Generated Solution

To solve the given problem, we need to find the sum \[ S = \sum_{r=1}^{\infty} \tan^{-1} \left( \frac{2(2r - 1)}{4 + r^2(r^2 - 2r + 1)} \right). \] ### Step 1: Simplify the Denominator ...
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sum_(i=1)^(oo)tan^(-1)((1)/(2r^(2)))=

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Knowledge Check

  • Find the value of sum_(r=0)^(oo) tan^(-1) ((1)/(1 + r + r^(2)))

    A
    `pi/4`
    B
    `pi/8`
    C
    `pi/10`
    D
    `pi/12`

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