Interval of Convergence Practice Problems
Practice Problems
P∞ xn
1. Find the interval of convergence for n=0 n! .
P∞
2. Determine the interval of convergence for n=0 xn .
3. Find the interval of convergence for ∞ xn
P
n=1 n
.
4. Use the ratio test to find the radius of convergence of ∞ xn
P
n=0 2n
.
P∞ (x−3)n
5. Determine the interval of convergence for n=0 n2 .
(−1)n xn
6. Find the interval of convergence for ∞
P
n=0 n
.
7. Determine the interval of convergence for ∞ xn
P
n=0 n3 .
(x+2)n
8. Find the interval of convergence for ∞
P
n=0 n!
.
(2x)n
9. Use the ratio test to find the radius of convergence of ∞
P
n=0 n!
.
(x−1)n
10. Determine the interval of convergence for ∞
P
n=0 n
.
11. Find the interval of convergence for ∞ xn
P
n=0 n2 +1 .
P∞ (x−5)n
12. Determine the interval of convergence for n=0 n2
.
(−x)n
13. Find the interval of convergence for ∞
P
n=0 n
.
(x+1)n
14. Find the interval of convergence for ∞
P
n=0 2n
.
P∞ xn
15. Determine the interval of convergence for n=0 n4 .
(x−2)n
16. Find the interval of convergence for ∞
P
n=0 n!
.
P∞ xn
17. Determine the interval of convergence for n=0 n2 +n .
P∞ (x−1)n
18. Find the interval of convergence for n=0 n3
.
P∞ xn
19. Determine the interval of convergence for n=0 n2 .
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Practice Problems
P∞ xn
1. Find the interval of convergence for n=0 n! .
P∞
2. Determine the interval of convergence for n=0 xn .
3. Find the interval of convergence for ∞ xn
P
n=1 n
.
4. Use the ratio test to find the radius of convergence of ∞ xn
P
n=0 2n
.
P∞ (x−3)n
5. Determine the interval of convergence for n=0 n2 .
(−1)n xn
6. Find the interval of convergence for ∞
P
n=0 n
.
7. Determine the interval of convergence for ∞ xn
P
n=0 n3 .
(x+2)n
8. Find the interval of convergence for ∞
P
n=0 n!
.
(2x)n
9. Use the ratio test to find the radius of convergence of ∞
P
n=0 n!
.
(x−1)n
10. Determine the interval of convergence for ∞
P
n=0 n
.
11. Find the interval of convergence for ∞ xn
P
n=0 n2 +1 .
P∞ (x−5)n
12. Determine the interval of convergence for n=0 n2
.
(−x)n
13. Find the interval of convergence for ∞
P
n=0 n
.
(x+1)n
14. Find the interval of convergence for ∞
P
n=0 2n
.
P∞ xn
15. Determine the interval of convergence for n=0 n4 .
(x−2)n
16. Find the interval of convergence for ∞
P
n=0 n!
.
P∞ xn
17. Determine the interval of convergence for n=0 n2 +n .
P∞ (x−1)n
18. Find the interval of convergence for n=0 n3
.
P∞ xn
19. Determine the interval of convergence for n=0 n2 .
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