Consider the series Σ k=0 ak= 8 2.3k k! AN k=0 1. Evaluate ao, a5, a10, a15, and a20. What does the limit lim ak appear to be and what does it mean for the convergence or divergence of the series? ∞04-31 2. Use the ratio test to determine whether the series converges or diverges. 3. Use any of your work above to determine whether the series k=0 k! 2.3k converges or diverges.

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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Consider the series Σ
k=0
ak=
AN
k=0
2.3k
k!
1. Evaluate ao, a5, a10, a15, and a20. What does the limit lim ak appear to be and what does it
mean for the convergence or divergence of the series?
004-31
2. Use the ratio test to determine whether the series converges or diverges.
3. Use any of your work above to determine whether the series
k=0
k!
2.3k
converges or diverges.
Transcribed Image Text:Consider the series Σ k=0 ak= AN k=0 2.3k k! 1. Evaluate ao, a5, a10, a15, and a20. What does the limit lim ak appear to be and what does it mean for the convergence or divergence of the series? 004-31 2. Use the ratio test to determine whether the series converges or diverges. 3. Use any of your work above to determine whether the series k=0 k! 2.3k converges or diverges.
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