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Interval of Convergence Practice Problems — 19 Exercises with Step‑by‑Step Solutions

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2025/2026 Written for academic year
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Course Calculus
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A set of 19 practice problems on intervals of convergence with complete solutions. Covers ratio test, endpoint checks, and convergence domains for series and geometric series. Designed for exam prep and mastery of convergence techniques.

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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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