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∑n=1∞3n\sum_{n=1}^{\infty}3^nn=1∑∞3n
Does this geometric series converge to a finite number?
∑n=1∞(13)n\sum_{n=1}^{\infty}\left( \frac{1}{3} \right) ^nn=1∑∞(31)n
To what value does ∑n=1∞5(15)n−1\sum_{n=1}^{\infty} 5 \left( \frac{1}{5} \right) ^{n-1}n=1∑∞5(51)n−1
converge?
Consider the series:
A. ∑n=1∞1n2\text{A. }\sum_{n=1}^{\infty} \frac{1}{n^2} A. n=1∑∞n21
B. ∑n=1∞1n\text{B. }\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}} B. n=1∑∞n1
∑n=1∞(−1)n\sum_{n=1}^{\infty} (-1)^n n=1∑∞(−1)n
Does this series converge?
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