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Can someone please help me with a problem for homework? I would really appreciate it.

So the problem I am given says:

Calculate ${\pi\over 2} - {\pi^3\over 2^33!} + {\pi^5\over 2^55!} -{\pi^7\over 2^77!} + ...$

So I did other problems like this, and in those problems I had to find a general expression for the given series and than match that expression to a known Maclaurin series expression and than solve it from there.

I am having trouble with this problem because I can't figure out the expression. Can someone please just give me some starting advice on how to go about solving this problem?

Thanks

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  • $\begingroup$ Do you recognize the series $x- {x^3\over 3!} + {x^5\over 5!} - {x^7 \over 7!}$? What happens if you replace $x$ with ${\pi\over 2}$? $\endgroup$ – user47693 Apr 22 '14 at 18:07
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The Maclaurin series for $\sin$ is $$\sin x = x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\ldots$$ The sum you are looking for is obtained when we put $x=\frac{\pi}{2}$ in this series.

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