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`6. Evaluate the following geometric series as exact numbers. If the series diverges, then state that it diverges and justify your conclusion. Ξ n=2 00 n=0 (Σ n=0 τ 11 p3-2n του 3(-2)" - 5" gn 4.) (d) 6 η=3 00 (Σ (7) n=1 η ηπο 1-n 8+2+1 5n+2

`6. Evaluate the following geometric series as exact numbers. If the series diverges, then state that it diverges and justify your conclusion. Ξ n=2 00 n=0 (Σ n=0 τ 11 p3-2n του 3(-2)" - 5" gn 4.) (d) 6 η=3 00 (Σ (7) n=1 η ηπο 1-n 8+2+1 5n+2

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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6. Evaluate the following geometric series as exact numbers. If the series diverges, then state that it diverges and justify your conclusion. (a) \(\sum_{n=2}^{\infty} 7 \left(-\frac{2}{11}\right)^n\) (b) \(\sum_{n=0}^{\infty} e^{3-2n}\) (c) \(\sum_{n=0}^{\infty} \frac{3(-2)^n - 5^n}{8^n}\) (d) \(\sum_{n=3}^{\infty} 6 \left(\frac{5}{3}\right)^{-n}\) (e) \(\sum_{n=1}^{\infty} \left(\frac{\pi}{e}\right)^{1-n}\) (f) \(\sum_{n=0}^{\infty} \frac{8 + 2^{n+1}}{5^{n+2}}\)
Transcribed Image Text:6. Evaluate the following geometric series as exact numbers. If the series diverges, then state that it diverges and justify your conclusion. (a) \(\sum_{n=2}^{\infty} 7 \left(-\frac{2}{11}\right)^n\) (b) \(\sum_{n=0}^{\infty} e^{3-2n}\) (c) \(\sum_{n=0}^{\infty} \frac{3(-2)^n - 5^n}{8^n}\) (d) \(\sum_{n=3}^{\infty} 6 \left(\frac{5}{3}\right)^{-n}\) (e) \(\sum_{n=1}^{\infty} \left(\frac{\pi}{e}\right)^{1-n}\) (f) \(\sum_{n=0}^{\infty} \frac{8 + 2^{n+1}}{5^{n+2}}\)
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