How is [itex]\lim_{n\rightarrow ∞} \frac{1-r^{N+1}}{1-r}[/itex] derived?(adsbygoogle = window.adsbygoogle || []).push({});

Is it directly related to [itex]S_{n}=\frac{a(1-r^{n})}{1-r}[/itex]?

If so, how does the [itex]r^{n}[/itex] become [itex]r^{n+1}[/itex]

and how does the a disappear?

I've seen how to derive [itex]S_{n}=\frac{a(1-r^{n})}{1-r}[/itex], but have never come across [itex]\lim_{n\rightarrow ∞} \frac{1-r^{N+1}}{1-r}[/itex] until I just came across a brief mention of it in a video.

Any suggestions on where I could find a derivation/proof for it?

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# How to derive [itex]\lim_{n\rightarrow ∞} \frac{1-r^{N+1}}{1-r}[/itex]

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