Proof of sum of first n terms, Sn

    If Sn represents the sum of the first n terms of a geometric series


        \[{S_n} = a + ar + a{r^2} + a{r^3} + a{r^4} + ... + a{r^{n - 1}}\]

    Note that the nth term is not arn but

        \[{{n^{th}}{\rm{ term}} = a{r^{n - 1}}}\]

    then it can be shown that the sum of the first n terms is given by Sn where

        \[{{S_n} = \frac{{a(1 - {r^n})}}{{1 - r}}}\]

You are expected to be able to prove this and so in this video, I show you how.

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