1
The Integral and Comparison Tests- HW Problems
Use the integral test to determine the convergence or divergence of the
following series.
ln(𝑛)
1. ∑∞
𝑛=1 𝑛
1
2. ∑∞
𝑛=1 3
𝑛
1
3. 1 + 4 + 4 + 41 + ⋯ + 41
1
+⋯
√2 √3 √4 √𝑛
1 2 3 4 𝑛
4.
2
+ 5
+ 10
+ 17
+ ⋯ + 𝑛2 +1
+⋯
Use the comparison test to determine the convergence or divergence
of the following series.
1
5. ∑∞
𝑛=1
𝑛2+𝑛+1
𝑛2+1
6. ∑∞
𝑛=2
𝑛3−1
Determine if the following series are convergent or divergent.
1
7. ∑∞
𝑛=2 𝑛𝑙𝑛(𝑛)
∞ cos2(𝑛)
8. ∑𝑛=1 2
𝑛
1
9. ∑∞
𝑛=1 3𝑛+1
The Integral and Comparison Tests- HW Problems
Use the integral test to determine the convergence or divergence of the
following series.
ln(𝑛)
1. ∑∞
𝑛=1 𝑛
1
2. ∑∞
𝑛=1 3
𝑛
1
3. 1 + 4 + 4 + 41 + ⋯ + 41
1
+⋯
√2 √3 √4 √𝑛
1 2 3 4 𝑛
4.
2
+ 5
+ 10
+ 17
+ ⋯ + 𝑛2 +1
+⋯
Use the comparison test to determine the convergence or divergence
of the following series.
1
5. ∑∞
𝑛=1
𝑛2+𝑛+1
𝑛2+1
6. ∑∞
𝑛=2
𝑛3−1
Determine if the following series are convergent or divergent.
1
7. ∑∞
𝑛=2 𝑛𝑙𝑛(𝑛)
∞ cos2(𝑛)
8. ∑𝑛=1 2
𝑛
1
9. ∑∞
𝑛=1 3𝑛+1
