Chapter 11 - Infinite Sequences and Series - Review - Concept Check - Page 824: 3

(a) A geometric series is a series in the form of $\Sigma_{n=0}^{\infty}ar^{n}$ with initial term $a$ and common ratio $r$. It converges if $|r| \lt 1$ . In that case, it converges to $\frac{a}{1-r}$ (b) A $p$-series is a series in the form of $\Sigma_{n=1}^{\infty}\frac{1}{n^{p}}$, where p is a constant . It converges if $p \gt1$

Work Step by Step

(a) A geometric series is a series in the form of $\Sigma_{n=0}^{\infty}ar^{n}$ with initial term $a$ and common ratio $r$. It converges if $|r| \lt 1$ . In that case, it converges to $\frac{a}{1-r}$ (b) A $p$-series is a series in the form of $\Sigma_{n=1}^{\infty}\frac{1}{n^{p}}$, where p is a constant . It converges if $p \gt1$

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