For , the geometric series equals . Approximate by integrating only the first three…

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

For ∣x∣<1|x|<1, the geometric series ∑n=0∞xn\sum_{n=0}^{\infty} x^{n} equals 11−x\frac{1}{1-x}. Approximate ∫00.211−t dt\displaystyle \int_{0}^{0.2} \frac{1}{1-t}\,dt by integrating only the first three nonzero terms of the series representation and report the result to three decimal places.

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