# A calculus problem by Upanshu Gupta

Calculus Level 3

$\large f(x) = \sum_{n=0}^{\infty}\dfrac{2^{2n-1}(-1)^{n}x^{n}\ln^{2n}(x^{2}+1)\sin^{n}(x)}{(2n)!}$ For $$f(x)$$ as defined above, find $\large \left \lfloor 10^{7} f\left(\dfrac{\pi}{2}\right)\right \rfloor.$

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