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30. Suppose that E-o Cnx" converges when x when x = 6. What can be said about the convergence or diver- = -4 and diverges gence of the following series? ( a) Σ C (b) 2 c,8" n=0 n=0 (d) 2 (-1)"c,9" n=0

30. Suppose that E-o Cnx" converges when x when x = 6. What can be said about the convergence or diver- = -4 and diverges gence of the following series? ( a) Σ C (b) 2 c,8" n=0 n=0 (d) 2 (-1)"c,9" n=0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem 30** Suppose that \(\sum_{n=0}^{\infty} c_n x^n\) converges when \(x = -4\) and diverges when \(x = 6\). What can be said about the convergence or divergence of the following series? - **(a)** \(\sum_{n=0}^{\infty} c_n\) - **(b)** \(\sum_{n=0}^{\infty} c_n 8^n\) - **(d)** \(\sum_{n=0}^{\infty} (-1)^n c_n 9^n\)
Transcribed Image Text:**Problem 30** Suppose that \(\sum_{n=0}^{\infty} c_n x^n\) converges when \(x = -4\) and diverges when \(x = 6\). What can be said about the convergence or divergence of the following series? - **(a)** \(\sum_{n=0}^{\infty} c_n\) - **(b)** \(\sum_{n=0}^{\infty} c_n 8^n\) - **(d)** \(\sum_{n=0}^{\infty} (-1)^n c_n 9^n\)
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