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Evaluating an infinite series Let f(x)= (cx 1 )/x for x 0
Chapter 8, Problem 46E(choose chapter or problem)
QUESTION:
Evaluating an infinite series Let \(f(x)=\left(e^{x}-1\right) / x\) for \(x \neq 0\) and f(0) = 1. Use the Taylor series for f and \(f^{\prime}\) about 0 to evaluate \(f^{\prime}(2)\) and to find the value of a \(\sum_{k=1}^{\infty} \frac{k 2^{k-1}}{(k+1) !}\).
Questions & Answers
QUESTION:
Evaluating an infinite series Let \(f(x)=\left(e^{x}-1\right) / x\) for \(x \neq 0\) and f(0) = 1. Use the Taylor series for f and \(f^{\prime}\) about 0 to evaluate \(f^{\prime}(2)\) and to find the value of a \(\sum_{k=1}^{\infty} \frac{k 2^{k-1}}{(k+1) !}\).
ANSWER:Solution 46EStep 1:Given thatLet f(x)= (cx 1 )/x for x 0 and f(0) = 1 Step2:To find Use the Taylor series for f and f' abo