Does the Euler-Mascheroni Constant Have a Limit as N Approaches Infinity?

[gnrlies00]

does the limit exists for

lim {$\sum\frac{1}{m}$ - ln N}; as N→∞, Ʃ is from m=1 to N

Please give me hints, on how to go about this problem

thanks

 

[HallsofIvy]

Look here:
http://mathworld.wolfram.com/Euler-MascheroniConstant.html