Question

Intervals of convergence...

Answer 1

Let f denote the sum function of power series, and let g denote the sum function of power series
\[f: \sum_{n=0}^{∞}\frac{ 1 }{ 1+a^n }x^n\]
\[g: \sum_{n=0}^{∞}\frac{ 1 }{ 1+a^{-n} }x^n\]
Show that:
\[f(x) + g(x)=\frac{ 1 }{ 1-x }\]
in the intersection interval of convergence.
Can someone help me?

Answer 2

@Mertsj @.Sam.