1
Geometric and Telescoping Series- HW Problems
Determine if the following geometric series converge of diverge. If they
converge find the sum.
1
1. ∑∞
𝑛=1
3𝑛
1 1 1
2. 1 −
4
+ 16
− 64
+⋯
𝑒𝑛
3. ∑∞
𝑛=1
2𝑛
(−1)𝑛
4. ∑∞
𝑛=1 𝑛
5
Determine if the following series are convergent or divergent. If it’s
convergent find the sum.
∞ 2𝑛−3𝑛
5. ∑𝑛=1 𝑛
4
∞ 2+4𝑛+1
6. ∑𝑛=1 𝑛
8
𝑛+1
7. ∑∞
𝑛=1 2𝑛+3
2
8. ∑∞
𝑛=1 cos (𝑛)
1 1 1 1 1
9. + + + + +⋯
2 4 6 8 10
Geometric and Telescoping Series- HW Problems
Determine if the following geometric series converge of diverge. If they
converge find the sum.
1
1. ∑∞
𝑛=1
3𝑛
1 1 1
2. 1 −
4
+ 16
− 64
+⋯
𝑒𝑛
3. ∑∞
𝑛=1
2𝑛
(−1)𝑛
4. ∑∞
𝑛=1 𝑛
5
Determine if the following series are convergent or divergent. If it’s
convergent find the sum.
∞ 2𝑛−3𝑛
5. ∑𝑛=1 𝑛
4
∞ 2+4𝑛+1
6. ∑𝑛=1 𝑛
8
𝑛+1
7. ∑∞
𝑛=1 2𝑛+3
2
8. ∑∞
𝑛=1 cos (𝑛)
1 1 1 1 1
9. + + + + +⋯
2 4 6 8 10
