Solution Found!
Interval and radius of convergence Determine
Chapter 8, Problem 19E(choose chapter or problem)
QUESTION:
Interval and radius of convergence Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.
\(\sum \frac{k^{20} x^{k}}{(2 k+1) !}\)
Questions & Answers
QUESTION:
Interval and radius of convergence Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.
\(\sum \frac{k^{20} x^{k}}{(2 k+1) !}\)
ANSWER:Solution 19E
Step 1:
In this problem we have to determine the radius of convergence of the power series.
Use Root test to determine the radius of convergence.
If and
- If L<1, converges.
- If L>1, diverges.
- If L=1, the test is inconclusive.