Consider the series ∞ (2x)n Σ n=1 n2 A) | Compute the limit: lim an+1 nx an Show your steps. B) | According to the Ratio Test, for what values of x is the series convergent? C) According to the Ratio Test, for what values of x is the series divergent?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 33E
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Consider the series
∞
(2x)n
Σ
n=1
n2
A)
| Compute the limit: lim
an+1
nx an
Show your steps.
B)
| According to the Ratio Test, for what values of x is the series convergent?
C) According to the Ratio Test, for what values of x is the series divergent?
Transcribed Image Text:Consider the series ∞ (2x)n Σ n=1 n2 A) | Compute the limit: lim an+1 nx an Show your steps. B) | According to the Ratio Test, for what values of x is the series convergent? C) According to the Ratio Test, for what values of x is the series divergent?
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