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# Why does the ln(x!)/x! , taking the sum from 0 to infinity, converge?

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• Why does the ln(x!)/x! , taking the sum from 0 to infinity, converge?

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Answer #1 | 11/08 2015 03:54
ln x! = ln x + ln (x-1) + ln (x-2) ... + ln 2 ln x < x for all x ln x! < x + x-1 + ... ln 2 ln x! < x^2 Sum x^2 / x! converges.
Positive: 50 %
Answer #2 | 10/08 2015 21:03
By the ratio test
Positive: 50 %
Answer #3 | 10/08 2015 20:54
ln x! = ln x + ln (x-1) + ln (x-2) ... + ln 2 ln x < x for all x ln x! < x + x-1 + ... ln 2 ln x! < x^2 Sum x^2 / x! converges.
Positive: 50 %
Answer #4 | 11/08 2015 04:03
By the ratio test
Positive: 50 %
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