An infinite geometric progression has first term and common ratio
MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series
Problem
An infinite geometric progression has first term 5 and common ratio −31.
(i) Obtain a simplified expression for the remainder after the first n terms.
(ii) Show that the sign of the remainder alternates as n increases.
(iii) Find the smallest positive integer n for which the magnitude of the remainder does not exceed 0.0001.