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Math Help - Finding sums involving Arctan

  1. #1
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    Finding sums involving Arctan

    Given that

    Arctan (1/n) - Arctan (1/(n+1)) = Arctan (1/((1+n(n+1))

    Find

    Sum from i = 1 to n:

    Arctan (1/((1+i(i+1))

    I have split the question into finding the sum of Arctan (1/n) and Arctan (1/(n+1)), and i'm pretty sure this is the correct approach, but I'm not sure where to go from here

    Thanks a lot
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  2. #2
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    Quote Originally Posted by Wandering View Post
    Given that
    Arctan (1/n) - Arctan (1/(n+1)) = Arctan (1/((1+n(n+1))
    Find
    Sum from i = 1 to n:
    Arctan (1/((1+i(i+1))
    Note that the sequence of partial sums is a sequence of collapsing sums.
    S_N=arctan(1)-arctan(1/(N+1)
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