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Solved: Evaluating an infinite series Write the Taylor
Chapter 8, Problem 48E(choose chapter or problem)
QUESTION:
Evaluating an infinite series Write the Taylor series for f(x) = In (1 + x) about 0 and find the interval of convergence. Evaluate \(f\left(-\frac{1}{2}\right)\) to find the value of \(\sum_{k=1}^{\infty} \frac{1}{k \cdot 2^{k}}\).
Questions & Answers
QUESTION:
Evaluating an infinite series Write the Taylor series for f(x) = In (1 + x) about 0 and find the interval of convergence. Evaluate \(f\left(-\frac{1}{2}\right)\) to find the value of \(\sum_{k=1}^{\infty} \frac{1}{k \cdot 2^{k}}\).
ANSWER:Solution 48EStep 1:Given thatf(a) = 1n (1 + a) about 0