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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 a, #0 then, the sequence {a} is divergent. (b) Suppose the infinite series a, is divergent. Then for any constant e, the series ca, is also divergent. (c) Let s, = a1 +. + an. If lim S = 0, then the series a, is convergent. WI

Write True if the statement is true. If the statement is false, explain briefly why it is so. (a) If lim a, #0 then, the sequence {a} is divergent. (b) Suppose the infinite series a, is divergent. Then for any constant e, the series ca, is also divergent. (c) Let s, = a1 +. + an. If lim S = 0, then the series a, is convergent. WI

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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Do as indicated. You are allowed to use only the theorems, definitions, and tests discussed during synchronous classes. I. Write True if the statement is true. If the statement is false, explain briefly why it is so. (a) If_lim a, #0 then, the sequence {an} is divergent. (b) Suppose the infinite series a, is divergent. Then for any constant e, the series ca, is n=1 also divergent. (c) Let s, = a1 +... + an. If lim s, = 0, then the series is convergent. an n=1
Transcribed Image Text:Do as indicated. You are allowed to use only the theorems, definitions, and tests discussed during synchronous classes. I. Write True if the statement is true. If the statement is false, explain briefly why it is so. (a) If_lim a, #0 then, the sequence {an} is divergent. (b) Suppose the infinite series a, is divergent. Then for any constant e, the series ca, is n=1 also divergent. (c) Let s, = a1 +... + an. If lim s, = 0, then the series is convergent. an n=1
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