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Write True if the statement is true. If the statement is false, explain briefly why it is so (a) If lim an # 0 then, the sequence {an} is divergent. (b) Suppose the infinite series an is divergent. Then for any constant c, the serie n=1 Σ E ca, is also divergent. n=1 (c) Let s, = a + ... + an. If lim s, = 0, then the series > an is convergent.

Write True if the statement is true. If the statement is false, explain briefly why it is so (a) If lim an # 0 then, the sequence {an} is divergent. (b) Suppose the infinite series an is divergent. Then for any constant c, the serie n=1 Σ E ca, is also divergent. n=1 (c) Let s, = a + ... + an. If lim s, = 0, then the series > an is convergent.

Advanced Engineering Mathematics
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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Write True if the statement is true. If the statement is false, explain briefly why it is so. (a) If lim an + 0 then, the sequence {an} is divergent. (b) Suppose the infinite series an is divergent. Then for any constant c, the series n=1 > ca, is also divergent. n=1 (c) Let s, = a1 +... + an. If lim s, = 0, then the series >a, is convergent. n +00
Transcribed Image Text:Write True if the statement is true. If the statement is false, explain briefly why it is so. (a) If lim an + 0 then, the sequence {an} is divergent. (b) Suppose the infinite series an is divergent. Then for any constant c, the series n=1 > ca, is also divergent. n=1 (c) Let s, = a1 +... + an. If lim s, = 0, then the series >a, is convergent. n +00
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