Use the results in Exercise 36 to find the sum of each series.(a) k=1(1)k+1 1k = 1 12
Chapter 9, Problem 38(choose chapter or problem)
Use the results in Exercise 36 to find the sum of each series.
\(\text { (a) } \sum_{k=1}^{\infty}(-1)^{k+1} \frac{1}{k}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots\)
\(\text { (b) } \sum_{k=1}^{\infty} \frac{(e-1)^{k}}{k e^{k}}=\frac{e-1}{e}+\frac{(e-1)^{2}}{2\left(e^{2}\right)}-\frac{(e-1)^{3}}{3\left(e^{3}\right)}+\cdots\)
Equation Transcription:
Text Transcription:
Sum of k=1 infinity (-1)^k=1 1/k=1-½+1/3+-¼+...
Sum of k=1 infinity (e-1)^k/ke^k=e-1/e+(e+1)^2/2)e^2)-(e-1)^3/3(e^3)+...
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