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Given that π=4∑k=1∞(−1)k+12k−1,\displaystyle \pi = 4\sum_{k=1}^{\infty} \frac{\left(-1\right)^{k+1}}{2k-1},π=4k=1∑∞2k−1(−1)k+1, what is the value of
∑n=1∞(π−4∑k=1n(−1)k+12k−1)?\sum_{n=1}^{\infty} \left( \pi - 4\sum_{k=1}^{n} \frac{\left(-1\right)^{k+1}}{2k-1} \right)?n=1∑∞(π−4k=1∑n2k−1(−1)k+1)?
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