Mathematics

Mathematics

Problem

During the derivation of the sum of the first nn terms of a GP with first term aa and common ratio r (r≠1)r\,(r\neq1), one arrives at rSn−Sn=arn−a.rS_n-S_n=ar^{n}-a. Which of the following is the correctly simplified expression for SnS_n obtained from this equation? a) a1−rnr−1a\dfrac{1-r^{n}}{r-1} b) rn−1r−1\dfrac{r^{n}-1}{r-1} c) arn−1r−1a\dfrac{r^{n}-1}{r-1} d) arn+1−1r−1a\dfrac{r^{n+1}-1}{r-1}

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