Sum of Infinite Geometric Sequence/Corollary 2/Mistake
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Source Work
1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics:
- 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.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): geometric series