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Evaluate
∑k=0∞(−1)k(14k+1+14k+3).{\displaystyle \sum_{k=0}^{\infty} (-1)^k \left(\frac{1}{4k+1} + \frac{1}{4k+3}\right)} .k=0∑∞(−1)k(4k+11+4k+31).
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