Show that the SERIES log k / (k^p), p>1 converges.
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Originally Posted by thahachaina Show that the SERIES log k / (k^p), p>1 converges.
thanks. Let be an infinite series with and . Then converges iff converges. So since and monotonically decreasing we may apply the above test. So . Now applying the Root test gives
So now for a series to converge we must have that
So solving this for p gives
Originally Posted by thahachaina Hey guys,
Does the SERIES, log k/ k^p, where p>1, converge or diverge???
Thanks It converges because increases more slowly than and so eventually:
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