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