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    Integral Test for Convergence

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    Solution. Consider the integral

    By the Integral Test, we know that converges.
    Why do we choose 2 NOT 1? Since when we choose 1, then ln1=0. So,

    Solution. Since , we have

    We know that diverges. So, by comparison test, we know that

    Method 2: The Integral Test

    Consider a integral

    So, diverges.

    3. Use the Integral Test instead of known results of geometric series.

    Solution. Consider the integral

    So, by the integral test, we know that converges.

    Also, we know it is a geometric series with |r|=1/e<1, so we know that converges.

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    Solution. Consider the integral

    By the ...

    Solution Summary

    The Integral Test for Convergence is investigated. The geometric series in integrals are provided.