(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am trying to prove the sum of a geometric series, but one of the steps involves deriving this result:

[tex]\lim_{n\to\infty}r^{n}=0[/tex]

so that you can simplify the sum of a geometric series, where I have got to this stage:

[tex]S_{\infty} = \frac{a(1-r^{\infty})}{1-r}[/tex]

2. Relevant equations

[tex]\lim_{n\to\infty}r^{n}=0[/tex]

s.

3. The attempt at a solution

I've managed to do the rest of the derivation and can continue past the above steps, by assuming that the limit does equal zero, but I am stuck on the proof. I've looked online and it seems you need calculus to prove this, but we've not been taught any.

I know the limit equals zero for r <|1|, as it makes sense intuitively, but how do I prove this or start to?

Thanks

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# Convergence Proof (As Part of Geometric Series Sum)

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