Which of the following series converges?
∑n=1∞(−1)n(n23n)\sum_{n=1}^{\infty} (-1)^n \left( \frac{n^2}{3\sqrt{n}} \right)∑n=1∞(−1)n(3nn2)
∑n=1∞(−1)n(n+12n)\sum_{n=1}^{\infty} (-1)^n \left( \frac{n + 1}{2n} \right)∑n=1∞(−1)n(2nn+1)
∑n=1∞(−1)n(2nn)\sum_{n=1}^{\infty} (-1)^n \left( \frac{2\sqrt{n}}{n} \right)∑n=1∞(−1)n(n2n)
∑n=1∞(−1)n(1−nn)\sum_{n=1}^{\infty} (-1)^n \left( \frac{1 - n}{n} \right)∑n=1∞(−1)n(n1−n)
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