Help Needed !

Two days ago a friend of mine shared with me a question stating that I couldn't solve that question and neither will anyone on Brilliant .

Darn him ! But he turned out to be partially correct , since I wasn't able to solve it and hence I am appealing to all the Brilliant minds out here to lend me your hand in solving the following question :

\[\displaystyle \huge \sum_{r=1}^{\infty} \sqrt{ \int_{0}^{\frac{\pi}{2}} \left ( 5+ \Gamma \left ( \dfrac{2}{2+x^{2r}} \right ) \right ) dx}\]

P.S. I tried using the Weirerstrass form and stuff , but was unsuccessful . I even posted this question in 3 communities in Google Plus , ends up that they got scared after seeing this question !

Best of Luck !!!

Note by Azhaghu Roopesh M
3 years, 1 month ago

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Is this gamma function, because if that is gamma function, then this sum doesn't converge.

Ronak Agarwal - 3 years, 1 month ago

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Yeah, I also think so!

Kartik Sharma - 3 years, 1 month ago

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Ok, sorry guys !! I didn't do the convergence test first !! I always forget to do it

Azhaghu Roopesh M - 3 years, 1 month ago

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What's the claim that it converges?

Kartik Sharma - 3 years, 1 month ago

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@Azhaghu Roopesh M , are you sure this question is solvable? Take it from a guy with experience, I once spent a whole day trying to prove Fermat's last theorem after my friend told me that I will never be able to solve it. Of course, I got to know that it was way out of my league the next day.

Raghav Vaidyanathan - 3 years, 1 month ago

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Turns out the sum doesn't converge , sorry !!

Tell me more about your trying to prove the Last theo , now you've got me interested :D

Azhaghu Roopesh M - 3 years, 1 month ago

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Can you please tell me something about that friend of yours, Is he studying in colledge, studying calculus. @Azhaghu Roopesh M

Ronak Agarwal - 3 years, 1 month ago

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Actually he's also in Class 12 and it was he who gave me that Find it's closed form question .

Azhaghu Roopesh M - 3 years, 1 month ago

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Comment deleted Mar 14, 2015

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The sum doesn't converge.

Krishna Sharma - 3 years, 1 month ago

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Yes, sorry abt that ! I didn't do the convergence test

Azhaghu Roopesh M - 3 years, 1 month ago

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Sorry Azhaghu i only know the basics of calculus.And its would be very hard for me to figure out this question...And I think there is a small typo in your mentioning...probably you mentioned Karthik instead of Kartik(I think)..Thanks

Anik Mandal - 3 years, 1 month ago

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Ah , yes .

Azhaghu Roopesh M - 3 years, 1 month ago

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