Prove that $1+x+x^2+...x^n=\frac{1-x^{n+1}}{1-x} $
and how to prove this implies that for $|x|<1$
$$1+x+x^2+........=\frac{1}{1-x}$$
for the first part we can prove by induction but to get second one by using first one
Prove that $1+x+x^2+...x^n=\frac{1-x^{n+1}}{1-x} $
and how to prove this implies that for $|x|<1$
$$1+x+x^2+........=\frac{1}{1-x}$$
for the first part we can prove by induction but to get second one by using first one