Answer to Question #258402 in Calculus for esty

Question

.A geometric series with first term 3 converges to the sum of 2. Find the common ratio of the series.

Answer 1

let $a=3$ be the 1st term and r be the common ratio ,so:

$S\infin=a/(1-r)$

$S\infin=3/(1-r)$

$S\infin=2$ $\therefore$

$2=3/(1-r)$

multiply both sides by $(1-r)$

$2(1-r)=3$

$2-2r=3$

$-2r=1$

$\therefore$ $r=-0.5$ is the correct answer.