3. Prove each of the following. (a) If a converges, then Ei, must diverge. 1+ ak (b) If an 20 for all k eN and a converges, then must converge. 1+ ak 1 (c) The series converges and its sum is at most 34 + k - 1 k=1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3. Prove each of the following.
(a) If Ea converges, then i must diverge.
1+ a.
(b) If ar 20 for all k e N and ar converges, then
must converge.
1+ ak
1
(c) The series
3k + k – 1
k=1
converges and its sum is at most
2
Transcribed Image Text:3. Prove each of the following. (a) If Ea converges, then i must diverge. 1+ a. (b) If ar 20 for all k e N and ar converges, then must converge. 1+ ak 1 (c) The series 3k + k – 1 k=1 converges and its sum is at most 2
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