Sum of Infinite Geometric Sequence/Corollary 2/Mistake

Source Work

 * geometric series
 * geometric series

Mistake

 * The sum of the finite initial segments of the series is:
 * $\dfrac {a \paren {r^n - 1} } {r - 1}$,
 * whence, if the infinite series converges, its sum is $a / \paren {r - 1}$.

Correction
This should read:


 * whence, if the infinite series converges, its sum is $a / \paren {1 - r}$.

This is demonstrated in Sum of Infinite Geometric Sequence: Corollary 2.