Consider the given integral: $$ \int_{0}^{1} (\sum_{n=1}^{\infty}\frac{\lfloor 2^n x\rfloor}{3^n})^2 \,dx $$ Please suggest how to approach this problem.
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This is an interesting problem, but you need to tell us what you have tried before we can help you. – Christian E. Ramirez Mar 23 '23 at 05:58
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I couldn't really do anything with it. That's why I felt stuck. – Srish Dutta Mar 23 '23 at 06:08
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1You should try anything, even if it doesn't work. Alternatively, if you really have no idea where to start, it would at least be a good idea to tell us where you found this integral.$\tag*{}$ If you want a hint about where to start, expand the square into a double-series, swap the double-series and integral, and try integrating each term. This may or may not lead to a solution. – Christian E. Ramirez Mar 23 '23 at 06:14
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1Alright, I will try that and if I don't succeed I'll ask again. Thanks! – Srish Dutta Mar 23 '23 at 06:15
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Attempt a graphical representation of the function under the integral sign (integrand). – Jean Marie Mar 23 '23 at 10:03
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1Please stop posting duplicates (and provide the source!) – metamorphy Mar 24 '23 at 06:11