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M. 33. 5k

M. 33. 5k

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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33.

### Geometric Series: Evaluation and Convergence #### Problems 21-42: Evaluate each geometric series or state that it diverges. 21. \(\sum_{k=0}^{\infty} \left(\frac{1}{4}\right)^k\) 22. \(\sum_{k=0}^{\infty} \left(\frac{3}{5}\right)^k\) 23. \(\sum_{k=0}^{\infty} \left(-\frac{9}{10}\right)^k\) 24. \(\sum_{k=1}^{\infty} \left(-\frac{2}{3}\right)^k\) 25. \(\sum 0.9^k\) 26. \(1 + \frac{2}{7} + \frac{2^2}{7^2} + \frac{2^3}{7^3} + \cdots\) 27. \(1 + 1.01 + 1.01^2 + 1.01^3 + \cdots\) 28. \(1 + \frac{1}{\pi} + \frac{1}{\pi^2} + \frac{1}{\pi^3} + \cdots\) 29. \(\sum_{k=1}^{\infty} e^{-2k}\) 30. \(\sum_{m=2}^{\infty} \frac{5}{2^m}\) 31. \(\sum_{k=1}^{\infty} 2^{-3k}\) 32. \(\sum_{k=3}^{\infty} \frac{3 \cdot 4^k}{7^k}\) 33. \(\sum_{k=4}^{\infty} \frac{1}{5^k}\) 34. \(\sum_{k=0}^{\infty} \left(\frac{4}{3}\right)^{-k}\) 35. \(\sum_{k=0}^{\infty} 3(-\pi)^{-k}\) 36. \(\sum_{k=1}^{\infty} (-e)^{-k}\) 37. \(1 + \frac{e}{\pi} + \frac{e^2}{\pi^2} + \frac{e^3}{\pi^3}
Transcribed Image Text:### Geometric Series: Evaluation and Convergence #### Problems 21-42: Evaluate each geometric series or state that it diverges. 21. \(\sum_{k=0}^{\infty} \left(\frac{1}{4}\right)^k\) 22. \(\sum_{k=0}^{\infty} \left(\frac{3}{5}\right)^k\) 23. \(\sum_{k=0}^{\infty} \left(-\frac{9}{10}\right)^k\) 24. \(\sum_{k=1}^{\infty} \left(-\frac{2}{3}\right)^k\) 25. \(\sum 0.9^k\) 26. \(1 + \frac{2}{7} + \frac{2^2}{7^2} + \frac{2^3}{7^3} + \cdots\) 27. \(1 + 1.01 + 1.01^2 + 1.01^3 + \cdots\) 28. \(1 + \frac{1}{\pi} + \frac{1}{\pi^2} + \frac{1}{\pi^3} + \cdots\) 29. \(\sum_{k=1}^{\infty} e^{-2k}\) 30. \(\sum_{m=2}^{\infty} \frac{5}{2^m}\) 31. \(\sum_{k=1}^{\infty} 2^{-3k}\) 32. \(\sum_{k=3}^{\infty} \frac{3 \cdot 4^k}{7^k}\) 33. \(\sum_{k=4}^{\infty} \frac{1}{5^k}\) 34. \(\sum_{k=0}^{\infty} \left(\frac{4}{3}\right)^{-k}\) 35. \(\sum_{k=0}^{\infty} 3(-\pi)^{-k}\) 36. \(\sum_{k=1}^{\infty} (-e)^{-k}\) 37. \(1 + \frac{e}{\pi} + \frac{e^2}{\pi^2} + \frac{e^3}{\pi^3}
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