Calculus

Limits of Sequences and Series

Infinite Series Warmup

         

n=13n\sum_{n=1}^{\infty}3^n

Does this geometric series converge to a finite number?

n=1(13)n\sum_{n=1}^{\infty}\left( \frac{1}{3} \right) ^n

Does this geometric series converge to a finite number?

To what value does n=15(15)n1\sum_{n=1}^{\infty} 5 \left( \frac{1}{5} \right) ^{n-1}

converge?

Consider the series:

A. n=11n2\text{A. }\sum_{n=1}^{\infty} \frac{1}{n^2}

B. n=11n\text{B. }\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}

n=1(1)n\sum_{n=1}^{\infty} (-1)^n

Does this series converge?

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