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Thread: The sum of the trigonometric series...?

  1. #1
    Super Member fardeen_gen's Avatar
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    The sum of the trigonometric series...?

    The sum ∑(from n = 1 to ∞) arctan [n/(n^4 - 2n^2 + 2)] is equal to:
    A) (arctan 2 + arctan 3)/4
    B) 4. (arctan 1)
    C) -π/16
    D) 3π/16

    More than one options may be correct.
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  2. #2
    Super Member fardeen_gen's Avatar
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    To be more precise, it is = ?
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  3. #3
    Super Member wingless's Avatar
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    Quote Originally Posted by fardeen_gen View Post
    The sum ∑(from n = 1 to ∞) arctan [n/(n^4 - 2n^2 + 2)] is equal to:
    A) (arctan 2 + arctan 3)/4
    B) 4. (arctan 1)
    C) -π/16
    D) 3π/16

    More than one options may be correct.
    None of them is correct.

    \sum_{n=1}^\infty \arctan \frac{n}{n^4-2n^2+2} \approx 1.072215


    A) \frac{\arctan 2 + \arctan 3}{4} \approx 0.58904

    B) 4 \arctan 1 = 4 \frac{\pi}{4} = \pi \approx 3.14159

    C) -\frac{\pi}{16} \text{ is negative \dots}

    D) \frac{3\pi}{16} \approx 0.58904
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  4. #4
    Super Member fardeen_gen's Avatar
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    One of the answers is definitely true - this was what my instructor told me. Are you sure wingless that the the given sum is not equal to any of the options??
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