Proof $sum_{nge1} frac{n!}{x(x+1)cdotdotscdot(x+n-1)}$ ($x>0$) convergence/divergence.
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First I noticed that the series can be rewritten to $sum_{nge1}frac1{binom{x}{n}}$ . Applying root test: $lim_{ntoinfty} left|frac{binom{x}{n+1}}{binom{x}{n}}right| = lim_{ntoinfty} left|frac{binom{x}{n} cdot frac{x-n}{n-1}}{binom{x}{n}}right| = 1 $ . This test is inconclusive. I'm trying hard to find a series to compare to the given one, but I can't seem to find one. Any hints? Thanks in advance!
calculus sequences-and-series
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asked Jan 7 at 18:29
Zachary Zachary
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