Finite geometric series
= Finite geometric series
For $r\ne1$, a finite geometric series satisfies
$$
\sum_{j=m}^n r^j=r^m\frac{1-r^{n-m+1}}{1-r}.
$$
= Finite geometric series
For $r\ne1$, a finite geometric series satisfies
$$
\sum_{j=m}^n r^j=r^m\frac{1-r^{n-m+1}}{1-r}.
$$