Series: show that the following limit exists

[dingobingo]

Hi All,

I've been struggling with find a solution for this series problem for the past few days. (See image)


I've tried using a power series representation for the partial sum 1+1/2+1/3+1/n which calculates to the power series for -ln(1-x)? i think i'm thrown off by the last term -ln(n) and how to integrate that into a nice series representation for the sum. Any help/hints will be greatly appreciated!

Thanks!

 

[Steven G]

Can we please see your work? Maybe you just have a simple error.

 

[Otis]

Hi dingobingo. Are you familiar with the Euler-Mascheroni constant? You don't need to find the limit; you only need to demonstrate that it exists.

?

 

[dingobingo]

Hi Otis! thanks so much for the hint! I haven't heard of the Euler-Mascheroni constant before but the form matches the problem exactly.