Solution Found!
Convergence parameter Find the values of the parameter p
Chapter 12, Problem 62E(choose chapter or problem)
58-65. Convergence parameter Find the values of the parameter p for which the following series converge.
\(\sum_{k=0}^{\infty} \frac{k ! p^{k}}{(k+1)^{k}}\)
Questions & Answers
QUESTION:
58-65. Convergence parameter Find the values of the parameter p for which the following series converge.
\(\sum_{k=0}^{\infty} \frac{k ! p^{k}}{(k+1)^{k}}\)
ANSWER:Problem 62EConvergence parameter Find the values of the parameter p for which the following series converge. SolutionStep 1In this problem we have to find the value of parameter p for which the series converge. Since the series has a factorial term, let us use ratio test.Ratio test:Let be a sequence of nonzero terms and let . Then 1. If L < 1 then is convergent.2. If L > 1 then is divergent. 3. If L = 1 then nothing can be said about the series. In other words, we say that the ratio is inconclusive.