Integrating a series with a square root

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Kruger
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What I'm trying is to rewrite this as on this webpage http://en.wikipedia.org/wiki/Series_(mathematics) under the topic "Some types of infinite series".

It would not be difficult if the square rood weren't there. Can somebody help. Thanks for any help.
 
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Can we solve this or is this just unsolvable? Or can one only find something by applying the Euler-Mclaurian formula?
 
You haven't stated what you are after exactly.