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Answers:

Big Willy

Guru

Karma Points: 2,004

(Middle Tennessee State University)

Date Posted: 5/16/2008 11:23:25 AM Status: Live

Asker's Rating: Lifesaver

Response:

To determine the radius of convergence for the series, we use a ratio test.

The ratio test states that

lim a _n+1 < 1 if it is convergent

n--∞ a_n

Where a_n is the part of the series that doesn't alternate. This is the limit of the absolute value of the ratio

So lets set up this ratio

lim x ⁿ⁺¹ * n^{n < 1}

n--∞ nⁿ⁺¹ xⁿ

Simplify

lim abs( x/ n) < 1

n--∞

Pull out the absolute value of x

abs(x) lim 1/n < 1

n--∞

0 < 1

This thing is true for all values of x then, so this converges on the open interval (-∞, ∞)

Our RADIUS of convergence is (b-a)/2 for open interval (a, b)

∞ - (-∞)

= ∞

Chaosriders

Sage

Karma Points: 4,646

(Jacksonville University)

Date Posted: 5/16/2008 11:39:24 AM Status: Live

Asker's Rating: Helpful

Response:

Root test

for all x value the limit is less than 1

so the radius of convergence is (-∞,∞)

"to be smart, one has to realize oneself as not smart" by Chaosriders

"IF One Can Accept A Wrong Answer As Lifesaver, Why Squandering Your Time For The Right One?"
by the Great Mathematician of All Time

Mr.Nash

Expert

Karma Points: 1,131

Date Posted: 5/16/2008 11:47:31 AM Status: Live

Asker's Rating: Helpful

Response:

note: i mean it converges for all values .

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