1. series

lim(n tending to infinity) (1/(n+1)+1/(n+2)+.....+1/6n)=

the sum of the above series is

i have done by graph and answer is coming out to be ln6

how should i solve theorotically

2. Re: series

$\displaystyle\lim_{n \to{+}\infty}{\left(\dfrac{1}{n+1}+\dfrac{1}{n+2}+ \ldots+\dfrac{1}{6n}\right)}=$

$\displaystyle\lim_{n \to{+}\infty}{\dfrac{1}{n}}\sum_{k=1}^{5n}\dfrac{1 }{1+k/n}=\int_0^5\dfrac{dx}{1+x}=\log 6$