1). State whether the statement is true, or give an example to show that it is false.If∞ n = 1anxnconverges, thenanxn → 0asn → ∞.i). True ii) False; consideran = 1n + 1 iii) False; consideran = n + 1False; consideran = nniv) False; consideran = 1n! please show all the work clearly .

Answered: Image /qna-images/answer/92820c7d-003e-47f8-a540-cb047948db0c.jpg

Answered: 1). State whether the statement is…

1). State whether the statement is true, or give an example to show that it is false. If ∞ n = 1anxn converges, then anxn → 0 as n → ∞. i). True

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.4: Mathematical Induction

Problem 46E

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Question

1). State whether the statement is true, or give an example to show that it is false.

∞

n = 1

a_nxⁿ

converges, then

a_nxⁿ → 0

n → ∞.

i). True

ii) False; consider

a_n =

n + 1

iii) False; consider

a_n = n + 1

False; consider

a_n = nⁿ

iv) False; consider

a_n =

please show all the work clearly .

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