Check for convergence and the sum to infinity o... - SS2 Mathematics Sequence and Series Question
Check for convergence and the sum to infinity of the series \(1 - 0.1 + 0.01 - 0.001 + \ldots\)
\(Given\ 1 - 0.1 + 0.01 - 0.001 + \ldots\), \(r = \frac{0.01}{- 0.1} = - \frac{1}{10}\), \(|r| = \frac{1}{10} < 1\)
This series converges
\[S_{\infty} = \frac{1}{1 - ( - 0.1)} = \frac{1}{1 + 0.1} = \frac{1}{1.1} = 0.909090\ldots\ \approx 0.91\]
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