For a finite geometric progression with first term and common ratio

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

Problem

For a finite geometric progression with first term

a

and common ratio

r\,(r\ne1)

, the sum of the first

n

terms is denoted by

S_{n}

. (i) Show that

S_{n}=a\dfrac{1-r^{n}}{1-r}

. (ii) Hence obtain an expression for the sum to infinity of the progression when

|r|<1

. (iii) Why can the expression found in part (ii) not be used when

|r|\ge1

? Give a brief justification.