Use the results in Exercise 36 to find the sum of the series.(a) k=1k3k = 13 +232 +333
Chapter 9, Problem 37(choose chapter or problem)
Use the results in Exercise 36 to find the sum of the series.
\(\text { (a) } \sum_{k=1}^{\infty} \frac{k}{3^{k}}=\frac{1}{3}+\frac{2}{3^{2}}+\frac{3}{3^{3}}+\frac{4}{3^{4}}+\cdots\)
\(\text { (b) } \sum_{k=1}^{\infty} \frac{1}{k\left(4^{k}\right)}=\frac{1}{4}+\frac{1}{2\left(4^{2}\right)}+\frac{1}{3\left(4^{3}\right)}+\frac{1}{4\left(4^{4}\right)}+\cdots\)
Equation Transcription:
Text Transcription:
Sum of k=1 infinity k/3^k = ⅓+⅔^2/+3/3^3+4/3^4+...
Sum of k=1 infinity 1/k(4^k)=¼+½(4^2)+⅓(4^3)+...
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