Question

Power Series representation.

Answer 1

\[\frac{ 1 }{ 1-x }=\sum_{n=0}^{\infty}x^n\]at first, is this correct ?

Answer 2

yes, but only for -1 < x < 1

Answer 3

ok, so for example if I got \[\frac{ x }{ 1-3x }\]then the power series representation is\[x \sum_{n=0}^{\infty}(3x)^n\]

Answer 4

(is this right ?)

Answer 5

yes, but this is only true for -1/3 < x < 1/3

Answer 6

ok ok, that is the interval of convergence...
all I care now about is power series rep.

tnx