Find the value of for which the infinite series has sum .

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

Problem

Find the value of

x

for which the infinite series

9+9x+9x^{2}+\dots

has sum

27

. (a)

-\dfrac{2}{3}

(b)

\dfrac{1}{3}

(c)

\dfrac{2}{3}

(d)

\dfrac{26}{27}