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I came across a theroem which says that if $S=(ar^{n-1}-a)/(r-1)$ when $r \neq 1$ then $S=(n+1)a$ if $r=1$. But for $r=1$ the above equation isn't well-defined. How do they come to this result?

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    Have a look at De l'Hôpital's Theorem.2012-10-24
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    It should be $S=(n-1)a,$ or $S=(ar^{n+1}-a)/(r-1)$.2012-10-24

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