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The Root Test Use the Root Test to determine
Chapter 12, Problem 23E(choose chapter or problem)
QUESTION:
19-26. The Root Test Use the Root Test to determine whether the following series converge.
\(\sum_{k=1}^{\infty}\left(\frac{k}{k+1}\right)^{2 k^{2}}\)
Questions & Answers
QUESTION:
19-26. The Root Test Use the Root Test to determine whether the following series converge.
\(\sum_{k=1}^{\infty}\left(\frac{k}{k+1}\right)^{2 k^{2}}\)
ANSWER:Problem 23E
The Root Test Use the Root Test to determine whether the following series converge.
Solution
Step 1
In this problem we have to determine whether the series converge or not by using root test.
Root test:
Let be a series of positive terms and let
- If then the series converges.
- If then the series diverges.
- If then the root test is inconclusive.