Determine the radius of convergence?
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Determine the radius of convergence?

[From: ] [author: ] [Date: 14-04-10] [Hit: ]
......

Σ (x^m/c^m) , c≠0
m=0

Assume c>0

-

Σ (x/c)^m , c≠0
m=0

This is a geometric sum, and converges when
|x/c| < 1
-1 < x/c < 1
-c < x < c

Radius of convergence = c
Interval of convergence -c < x < c

-
sum_m=0^infinity (x/c)^m = 1/(1 - (x/c)) = c/(c - x)

from the formula

sum_k=s^infinity (a*r^k) = (a*r^s)/(1 - r)

s = 0; r = x/c; a = 1
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