How Do You Determine the Interval of Convergence for a Series?

[knv]

1. Find the radius and the interval of convergence for the series:

Ʃ n=2 --> inf : [(-1)ⁿxⁿ]/ [4ⁿln(n)]





2.To find the radius, we use the alternating series test. **a_n+1/a_n




3. From the alternating series test I find that the limit as n --> inf = 4. So our radius is 4. Although I do not know how to get the intervals from the radius. Can anyone help me?

Would we just plug in ±4 for x and solve for convergence or divergence?

 

[LCKurtz]

1. Find the radius and the interval of convergence for the series:

Ʃ n=2 --> inf : [(-1)ⁿxⁿ]/ [4ⁿln(n)]





2.To find the radius, we use the alternating series test. **a_n+1/a_n

You mean the ratio test.

3. From the alternating series test I find that the limit as n --> inf = 4. So our radius is 4. Although I do not know how to get the intervals from the radius. Can anyone help me?

Would we just plug in ±4 for x and solve for convergence or divergence?

Yes. You know you have convergence for $-4 < x < 4$. So just check to see which, if any, of the end points to include.