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　$n$を自然数とする．
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\item[(1)]$\displaystyle \lim_{x \to 0} \frac{\sin (2n+1)x}{\sin x}$を求めよ．
\item[(2)]$\displaystyle \int_0^\frac{\pi}{2} \frac{\sin (2n+1)x}{\sin x}dx = \frac{\pi}{2}$を示せ．
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