I. Write True if the statement is true. If the statement is false, explain briefly why it is so.(a) Suppose the infinite series ) an is divergent. Then for any constant c, the seriesn=1> can is also divergent.n=1(b) Let sn = a1 + ... + an. If lim sn =0, then the series ) an is convergent.n=1(c) Given the alternating series (-1)"an. If an is increasing orlim an #0 then then→+0n=1given series is divergent.

The given question is related with series. Given three statements. (a) Suppose the infinite…

I. Write True if the statement is true. If the statement is false, explain briefly why it is so. 00 (a) Suppose the infinite series an is divergent. Then for any constant c, the series n=1 Σ can is also divergent. n=1 (b) Let sn = a1 + ... + an. If lim sn =0, then the series ) an is convergent. n-+00 n=1 (c) Given the alternating series)(-1)"an. If an is increasing or lim an #0 then the n=1 given series is divergent.

I. Write True if the statement is true. If the statement is false, explain briefly why it is so. 00 (a) Suppose the infinite series an is divergent. Then for any constant c, the series n=1 Σ can is also divergent. n=1 (b) Let sn = a1 + ... + an. If lim sn =0, then the series ) an is convergent. n-+00 n=1 (c) Given the alternating series)(-1)"an. If an is increasing or lim an #0 then the n=1 given series is divergent.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 67E

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