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Get an approximation formula for the following integral: $$ \sum_{k=1}^n \left( \frac{1}{35} \right)^{k-1}\int_0^{\frac{\pi}{2}}\cos^{2(n-k)+1}(y) \cdot \sin^{2(k-1)}(y) \, dy $$

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    Evaluating the integral could be a start. Use the Beta function.2011-12-27
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    @David Did you mean $\cos^{2(n-k)+1}\left( \sin^{2(k-1)}(y) \right) \mathrm{d}y$ or $\cos^{2(n-k)+1}(y) \cdot \sin^{2(k-1)}(y) \cdot \mathrm{d}y$ ?2011-12-27
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    $\cos^{2(n-k)+1}\cdot\sin^{2(k-1)}ydy$2011-12-27
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    @Patrick To the OP's credit, they do ask in a comment how to accept answers in this site. :) // David: In each answer for your questions, under the vote count will be a grey V-shaped tick mark. Clicking it will accept the answer. [You can also unaccept answers subsequently; just click the tick mark once again.]2011-12-27
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    @Srivastan : I didn't make my comment with respect to david's comment, but with respect to his (mathematical) question in the first place. His question in the comments was fine!2011-12-27
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    @Srivastan: Thank you very much.2011-12-27

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