2 (a) Use the Comparison Test to show that the series En-1 4n3n²+3 converges. (You may use the fact that the series 1 converges if k > 1 and diverges if 0 < k < 1.) 3n (b) Use the Ratio Test to decide whether the series Σ=1 4√√n converges or diverges. (c) Use the Alternating Series Test to show that the series En-1 2-1 converges.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3
2 (a) Use the Comparison Test to show that the series n=1 4n3n²+3 converges. (You may use the fact
n°-1
1
that the series -1 converges if k > 1 and diverges if 0 < k < 1.)
n=1
3n
(b) Use the Ratio Test to decide whether the series -1 4√n converges or diverges.
converges.
(-1)"
(c) Use the Alternating Series Test to show that the series n=1 2n-1
Transcribed Image Text:3 2 (a) Use the Comparison Test to show that the series n=1 4n3n²+3 converges. (You may use the fact n°-1 1 that the series -1 converges if k > 1 and diverges if 0 < k < 1.) n=1 3n (b) Use the Ratio Test to decide whether the series -1 4√n converges or diverges. converges. (-1)" (c) Use the Alternating Series Test to show that the series n=1 2n-1
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