The first term of an infinite geometric series is and its common ratio is

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

The first term of an infinite geometric series is

3

and its common ratio is

\dfrac{k-2}{k+1}

. For which values of

k

does the series converge? (a)

k>-1,\;k\neq -1

(b)

k>\dfrac12

(c)

k<\dfrac12

(d)

k\ge \dfrac12