Consider the telescoping series k=3 (a) Apply the Divergence Test to the series. Show all details. What conclusions, if any, can you make about the series? (b) Write out the partial sums 83, 84, 85, and s6. (c) Compute the n-th partial sum sn, and put it in closed form. (d) Determine if the series converges, and if so, what it converges to. If the series diverges, state whether it diverges to +∞, –∞, or neither.

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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2.
Consider the telescoping series
Č (VR – VR - 2)
k=3
(a) Apply the Divergence Test to the series. Show all details. What conclusions,
if any, can you make about the series?
(b) Write out the partial sums s3, s4, 85,
and
S6.
(c) Compute the n-th partial sum sn, and put it in closed form.
(d) Determine if the series converges, and if so, what it converges to. If the series
diverges, state whether it diverges to +o, –∞, or neither.
Transcribed Image Text:2. Consider the telescoping series Č (VR – VR - 2) k=3 (a) Apply the Divergence Test to the series. Show all details. What conclusions, if any, can you make about the series? (b) Write out the partial sums s3, s4, 85, and S6. (c) Compute the n-th partial sum sn, and put it in closed form. (d) Determine if the series converges, and if so, what it converges to. If the series diverges, state whether it diverges to +o, –∞, or neither.
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