# find the limit of a sequence

I try to find the limit of the sequence: $X_n =\displaystyle\sum_{k=1}^n\frac{1}{k} - \ln(n)$.

I try to find it on WolfarmAlpha, but It didn't reconize this limit.

Thank you

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Do you mean $X_n=\displaystyle\sum_{k=1}^n\frac{1}{k}-\ln n$? – Paul Jan 13 '12 at 13:50
@Paul: Yes. Thanks. – Adam Sh Jan 13 '12 at 13:51
I have edited your post. Please check if this is what you would like to ask. Thanks. – Paul Jan 13 '12 at 13:54
Harmonic Number – pedja Jan 13 '12 at 13:54
The limit is called the Euler–Mascheroni constant, but it has no known closed form, and this limit is basically its definition. See: en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant – Thomas Andrews Jan 13 '12 at 13:56

Euler's constant is $\lim \limits_{n\to \infty } \displaystyle\sum_{k=1}^n\frac{1}{k} - \ln(n)%$.it is very famous in number theory and analytic number theory.Euler's constant is open problem just we can show this series is converges.
If you need to show existence of the limit, show that $X_n$ is decreasing and bounded below.