Question

limit

Answer 1

show that there is a limit between 1/2 and 1\[\lim_{x \rightarrow \infty}(1+\frac{ 1 }{ 2 }+\frac{ 1 }{ 3 }+...+\frac{ 1 }{ n }-\log(n))\]

Answer 2

i notice \[\lim_{x \rightarrow \infty} \sum_{x=1}^{n}\frac{ 1 }{ n }-\lim_{x \rightarrow \infty}\log(n)\]

Answer 3

these is eulers constant\[\Gamma \]

Answer 4

Unfortunately I cannot solve this but I found something interesting about this limit - it converges to the Euler-Mascheroni Constant. See here: http://mathworld.wolfram.com/Euler-MascheroniConstant.html

Answer 5

good one @asnaseer,thanks