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Math Help - test for convergence

  1. #1
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    test for convergence

    find the sum of arcsin(1/square root n.) from n =1 to infinity.

    i think arcsin(1/square root n.) is approx arcsin(1/square root n).

    i tried using the limit comaprison test but it did not work for me
    I think im just confused.
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  2. #2
    MHF Contributor matheagle's Avatar
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    I don't know what ...arcsin(1/square root n.) is approx arcsin(1/square root n)... means

    DIVERGENT. Limit comp to \sum {1\over \sqrt{n}}. Let m={1\over \sqrt{n}}

    Then \lim_{n\to\infty}{ {1\over \sqrt{n} }\over \arcsin {1\over \sqrt{n}}} =\lim_{m\to 0^+}{m\over \arcsin m}=\lim_{m\to 0^+}\sqrt {1-m^2}=1.
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