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Math Help - Infinite series (4)

  1. #16
    Member Miss's Avatar
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    Quote Originally Posted by NonCommAlg View Post
    you should know that the convergence of \int^{\infty} f(x) \ dx doesn't necessarily imply that \sum^{\infty} f(n) is convergent. for example \int_0^{\infty} \sin x^2 \ dx=\sqrt{\frac{\pi}{8}} but the series \sum_{n=0}^{\infty} \sin n^2 is divergent.
    Ohh.
    But the integral test said that "if and only if".
    Maybe it implies the convergence only when function is positive,continuous and decreasing. Right?
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  2. #17
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    when i read the "maybe," then yes.
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  3. #18
    Member Miss's Avatar
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    Quote Originally Posted by Krizalid View Post
    when i read the "maybe," then yes.

    Sorry, but your reply did not make any sense.
    Is true or not ?
    forget that "maybe".
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  4. #19
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    true.
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