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Math Help - Proving the ratio test fails.

  1. #1
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    Proving the ratio test fails.

    Can anyone prove that the ratio test is inconclusive when

    \lim_{n \rightarrow \infty} |\frac{a_{n+1}}{a_{n}}| = 1, or

    \lim_{n \rightarrow \infty} |\frac{a_{n+1}}{a_{n}}| DNE.
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  2. #2
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    For the first one take a_n= \frac{1}{n} and b_n= \frac{1}{n^2} both limits are 1, but one converges and the other diverges. For the second I'm not sure...
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