MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series
Problem
Consider the infinite series
S=7−1.4+0.28−0.056+0.0112−…
(a) Identify the first term and common ratio of the series.
(b) Verify that the series converges or diverges. Cite all relevant conditions in your reasoning.
(c) Find the exact value of S expressed as a fraction in simplest form.
(d) Compute a decimal approximation of S correct to three decimal places.