Consider the infinite series S= _ n=2 ^ 9 ( 23 )^ n+1

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

Problem

Consider the infinite series

S=\sum_{n=2}^{\infty} 9\left(\frac23\right)^{n+1}.

Answer the following questions about

S

. (a) Write the

n

-th term of

S

in the form

ar^{n}

for some constants

a

and

r

whose values do not depend on

n

. (b) State the value of the common ratio

r

and the first term of the rewritten series. (c) Explain, with justification, whether the series

S

converges or diverges.