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Let $$f_n = \int_0^{\pi/2} \sum_{k=1}^{n} \sin^{k-1}x \sum_{k=1}^{n} (2k-1)\sin^{k-1}x \cos x \ dx$$, $$n \in \mathbb{N}$$. Then $$f_{21} - f_{20}$$ is equal to _____.
Correct Answer: 41
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