Which of the following is the correct expression for the sum to infinity of an…

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

Problem

Which of the following is the correct expression for the sum to infinity

S_{\infty}

of an infinite geometric progression with first term

a

and common ratio

r

(|r|<1)

? (a)

\displaystyle S_{\infty}=\frac{a}{1+r}

(b)

\displaystyle S_{\infty}=\frac{ar}{1-r}

(c)

\displaystyle S_{\infty}=\frac{a}{1-r}

(d)

\displaystyle S_{\infty}=\frac{a}{1-r^{2}}