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Infinite GP as a Limit
## Formula
For:
$$S_n=a\frac{1-r^n}{1-r}$$
if:
$$|r|<1$$
then:
$$\lim_{n\to\infty}r^n=0$$
Therefore:
$$S_\infty=\lim_{n\to\infty}S_n=\frac{a}{1-r}$$
## Usage
- Used to connect finite GP sums with infinite geometric series.
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Infinite GP as a Limit
## Formula
For:
$$S_n=a\frac{1-r^n}{1-r}$$
if:
$$|r|<1$$
then:
$$\lim_{n\to\infty}r^n=0$$
Therefore:
$$S_\infty=\lim_{n\to\infty}S_n=\frac{a}{1-r}$$
## Usage
- Used to connect finite GP sums with infinite geometric series.
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