An infinite geometric series has first term and positive common ratio

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

An infinite geometric series has first term

6

and positive common ratio

r

. The sum to infinity is known to be

15

. (i) Show that

r

satisfies the equation

\dfrac{6}{1-r}=15

. (ii) Solve the equation obtained in part (i) to find all possible values of

r

. (iii) From the values found in part (ii), identify the one that actually gives a convergent series and state a brief reason for your choice.