Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 12 - Section 12.3 - Geometric Sequences - 12.3 Exercises - Page 864: 4


Fill the blaks with a. ... $a\displaystyle \cdot\frac{1-r^{n}}{1-r}$ ... b. ... geometric... converges ...$\displaystyle \frac{a}{1-r}$... diverges

Work Step by Step

a. See p. 861. For the geometric sequence $a_{n}=ar^{n-1}$ the nth partial sum$ S_{n}=\displaystyle \sum_{k=1}^{n}ar^{k-1}$ (where $r\neq 1$) is given by$ \displaystyle \quad S_{n}=a\cdot\frac{1-r^{n}}{1-r}$ ====================== Fill the blank with $a\displaystyle \cdot\frac{1-r^{n}}{1-r}$ b. See p. 863. An infinite geometric series is a series of the form $ a+ar+ar^{2}+ar^{3}+\cdots+ar^{n-1}+\cdots$ An infinite geometric series for which $|r| < 1$ converges, and has the sum $S=\displaystyle \frac{a}{1-r}$ If $|r| \geq 1$, the series diverges (the sum does not exist). ==================== Fill the blanks with ... geometric... converges ...$\displaystyle \frac{a}{1-r}$... diverges
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