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Chapter 10: Q. 49 (page 777)

\[\sum\limits_{k = 1}^{k = \infty } {\frac{{{k^p}}}{{{e^k}}}} \]

Short Answer

Expert verified

the values of p are

Step by step solution

01

Step 1. Applying convergent series test

Given series :

\[\sum\limits_{k = 1}^{k = \infty } {\frac{{{k^p}}}{{{e^k}}}} \]

Let us apply ratio convergence test:

let \[{a_k}\]=\[\sum\limits_{k = 1}^{k = \infty } {\frac{{{k^p}}}{{{e^k}}}} \]

and \[{a_k+1}\] =\[\sum\limits_{k = 1}^{k = \infty } {\frac{{{k+1^p}}}{{{e^k+1}}}} \]

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