For a GP with first term and common ratio

MATHEMATICS · Subjective · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

For a GP with first term

a

and common ratio

r\,(r\neq1)

, let

S_{n}

denote the sum of its first

n

terms and

S_{n}'

denote the sum of the reciprocals of its first

n

terms. (a) Derive an expression for

S_{n}

in terms of

a,\,r

, and

n

. (b) Obtain a simplified expression for

S_{n}'

in terms of

a,\,r

, and

n

. (c) Hence, show that the product

S_{n}\,S_{n}'

is independent of the first term

a

and simplify this product as much as possible.