My Math Forum Really confusing problem asociated with riemann sum and integrals

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 September 27th, 2014, 11:32 AM #1 Member   Joined: Nov 2013 Posts: 34 Thanks: 1 Really confusing problem asociated with riemann sum and integrals Hello guys, could you help me with this? Express: $\displaystyle \lim_{n \rightarrow \infty}\sum_\left(i=1\right)^n \left(\frac{m_{i}+10}{m_{i}}\right) \frac{40}{n}$ as an definite integral in the interval [10,20] knowing that this sum is asociated with a Pn Partition of the interval [10,20] with n subintervals with same length, taking the half point m1 in each subinterval. And this have another exercise related: If you consider another P'n partition which takes the left extrem (not the half point) in each subinterval, will the limit be the same? I'd really thank you if you help me with this guys because I have no idea how to solve it!

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