Explanation Given: (a) ∑ n = 0 ∞ 7 n 29 n (b) ∑ n = 3 ∞ 1 n 4 (c) ∑ n = 0 ∞ n 2 2 n (d) ∑ n = 5

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ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 11.2, Problem 43E

To determine

Those out of the following series, which are not geometric series.

(a) $\sum_{n = 0}^{\infty} \frac{7^{n}}{29^{n}}$

(b) $\sum_{n = 3}^{\infty} \frac{1}{n^{4}}$

(c) $\sum_{n = 0}^{\infty} \frac{n^{2}}{2^{n}}$

(d) $\sum_{n = 5}^{\infty} π^{- n}$

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Chapter 11.2, Problem 42E

Chapter 11.2, Problem 44E

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Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

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Those out of the following series, which are not geometric series. (a) ∑ n = 0 ∞ 7 n 29 n (b) ∑ n = 3 ∞ 1 n 4 (c) ∑ n = 0 ∞ n 2 2 n (d) ∑ n = 5 ∞ π − n

Solution Summary: The author explains that it is not a geometric series because we cannot find the common ratio.

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Those out of the following series, which are not geometric series.

(a) $\sum_{n = 0}^{\infty} \frac{7^{n}}{29^{n}}$

(b) $\sum_{n = 3}^{\infty} \frac{1}{n^{4}}$

(c) $\sum_{n = 0}^{\infty} \frac{n^{2}}{2^{n}}$

(d) $\sum_{n = 5}^{\infty} π^{- n}$

Want to see the full answer?

Chapter 11 Solutions

Those out of the following series, which are not geometric series. (a) ∑ n = 0 ∞ 7 n 29 n (b) ∑ n = 3 ∞ 1 n 4 (c) ∑ n = 0 ∞ n 2 2 n (d) ∑ n = 5 ∞ π − n

Solution Summary: The author explains that it is not a geometric series because we cannot find the common ratio.

Concept explainers

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Those out of the following series, which are not geometric series. (a) ∑n=0∞7n29n (b) ∑n=3∞1n4 (c) ∑n=0∞n22n (d) ∑n=5∞π−n

Want to see the full answer?

Chapter 11 Solutions

Those out of the following series, which are not geometric series.

(a) $\sum_{n = 0}^{\infty} \frac{7^{n}}{29^{n}}$

(b) $\sum_{n = 3}^{\infty} \frac{1}{n^{4}}$

(c) $\sum_{n = 0}^{\infty} \frac{n^{2}}{2^{n}}$

(d) $\sum_{n = 5}^{\infty} π^{- n}$