1
Power Series- HW Problems
Find the radius of convergence and the interval of convergence for the
following series.
(−1)𝑛 𝑥𝑛
1. ∑∞
𝑛=1 2𝑛
∞ (−1)𝑛 𝑥𝑛
2. ∑𝑛=1 2 𝑛
𝑥𝑛
3. ∑∞
𝑛=1 𝑛!
∞ 𝑥𝑛
4. ∑𝑛=1
𝑛2 (3(𝑛+1) )
∞ 2𝑛
5. ∑𝑛=1 3 (𝑥 − 1 )𝑛
𝑛2
1
6. ∑∞
𝑛=1 3 (𝑥 + 3)𝑛
𝑛 +1
𝑛2
7. ∑∞
𝑛=1 𝑛 (𝑥 − 2)
𝑛
5
(−1)𝑛
8. ∑∞
𝑛=1 (𝑥 + 1)(2𝑛−1)
3𝑛+1
Power Series- HW Problems
Find the radius of convergence and the interval of convergence for the
following series.
(−1)𝑛 𝑥𝑛
1. ∑∞
𝑛=1 2𝑛
∞ (−1)𝑛 𝑥𝑛
2. ∑𝑛=1 2 𝑛
𝑥𝑛
3. ∑∞
𝑛=1 𝑛!
∞ 𝑥𝑛
4. ∑𝑛=1
𝑛2 (3(𝑛+1) )
∞ 2𝑛
5. ∑𝑛=1 3 (𝑥 − 1 )𝑛
𝑛2
1
6. ∑∞
𝑛=1 3 (𝑥 + 3)𝑛
𝑛 +1
𝑛2
7. ∑∞
𝑛=1 𝑛 (𝑥 − 2)
𝑛
5
(−1)𝑛
8. ∑∞
𝑛=1 (𝑥 + 1)(2𝑛−1)
3𝑛+1
