∞
Σ (x^m/c^m) , c≠0
m=0
Assume c>0
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
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
from the formula
sum_k=s^infinity (a*r^k) = (a*r^s)/(1 - r)
s = 0; r = x/c; a = 1