Let a geometric progression have first term and common ratio

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

Problem

Let a geometric progression have first term

a=8

and common ratio

r=\dfrac14

. (a) Write the sum

S_{n}

of its first

n

terms. (b) Calculate the sum to infinity of the progression. (c) Evaluate

S_{6}

and compare it with the value obtained in part (b). What does this comparison suggest about the convergence of the series?