The first term of an infinite geometric progression is and its common ratio is

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

The first term of an infinite geometric progression is

10

and its common ratio is

\tfrac35

. (i) Write an expression for the remainder after the first

n

terms are taken. (ii) Determine the least positive integer

n

for which this remainder is less than

0.01