- #1
raopeng
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- 0
Homework Statement
Find the sum using integration: [itex]lim_{n→∞} \frac{n}{(n+1)^2} + ... + \frac{n}{(2n)^2}[/itex]
Homework Equations
The Attempt at a Solution
I think this requires a clever construction of a series of an finite integral which after integration gives the series. Then it can be solved by summing up the series inside the integral then integrate the whole thing. But now what is bothering me is how to construct such a function, every function I have tried seems remotely far from the series in the question. Thanks for your time.