2. Prove that the following infinite series diverges. Σ(-1)*. k=1 (Hint: write down the first few partial sums, and prove that the sequence of partial sums diverges using the formal definition of divergence for a sequence. You could consider two cases for the supposed limit L, L > 0 and L ≤0, and show that in each case, there exists suitably small & that witnesses the divergence of the sequence).
2. Prove that the following infinite series diverges. Σ(-1)*. k=1 (Hint: write down the first few partial sums, and prove that the sequence of partial sums diverges using the formal definition of divergence for a sequence. You could consider two cases for the supposed limit L, L > 0 and L ≤0, and show that in each case, there exists suitably small & that witnesses the divergence of the sequence).
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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Transcribed Image Text:2. Prove that the following infinite series diverges.
Σ(-1)*.
k=1
(Hint: write down the first few partial sums, and prove that the sequence of partial
sums diverges using the formal definition of divergence for a sequence. You could
consider two cases for the supposed limit L, L > 0 and L ≤ 0, and show that in each
case, there exists suitably small & that witnesses the divergence of the sequence).
€
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