Solution Found!
Answer: Convergence parameter Find the values of the
Chapter 12, Problem 60E(choose chapter or problem)
58-65. Convergence parameter Find the values of the parameter p for which the following series converge.
\(\sum_{k=2}^{\infty} \frac{1}{k \ln k(\ln \ln k)^{p}}\)
Questions & Answers
QUESTION:
58-65. Convergence parameter Find the values of the parameter p for which the following series converge.
\(\sum_{k=2}^{\infty} \frac{1}{k \ln k(\ln \ln k)^{p}}\)
ANSWER:Problem 60E
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 integral test to find p .
INTEGRAL TEST DEFINITION; Suppose f is continuous , positive , decreasing function on[1, ) , and let
= f(n) . Then the convergence or divergence of the series
Is the same as that of the integral f(x) dx .
-
If
f(x) dx is convergent , then
is convergent .
-
If
That is bothand
converge or diverge together.