1
Sequences- HW Problems
Find the limit of the following sequences if they exit. If the sequence
diverges, say so.
2𝑛2 +1
1. 𝑎𝑛 = 2
𝑛 +3
𝑛3 +𝑛
2. 𝑎𝑛 =
𝑛2 +3
(−1)𝑛
3. 𝑎𝑛 =
ln(𝑛)
𝑛4
4. 𝑎𝑛 = 𝑛
2
𝑛𝑛
5. 𝑎𝑛 =
𝑛!
1
6. 𝑎𝑛 = sin ( )
𝑛+1
7. 𝑎𝑛 = 𝑒−𝑛
1
8. 𝑎𝑛 = (−1)𝑛 𝑒𝑛
4𝑛
9. 𝑎𝑛 = 𝑛
5
𝑛3
10. 𝑎𝑛 =
√𝑛5 +3
Sequences- HW Problems
Find the limit of the following sequences if they exit. If the sequence
diverges, say so.
2𝑛2 +1
1. 𝑎𝑛 = 2
𝑛 +3
𝑛3 +𝑛
2. 𝑎𝑛 =
𝑛2 +3
(−1)𝑛
3. 𝑎𝑛 =
ln(𝑛)
𝑛4
4. 𝑎𝑛 = 𝑛
2
𝑛𝑛
5. 𝑎𝑛 =
𝑛!
1
6. 𝑎𝑛 = sin ( )
𝑛+1
7. 𝑎𝑛 = 𝑒−𝑛
1
8. 𝑎𝑛 = (−1)𝑛 𝑒𝑛
4𝑛
9. 𝑎𝑛 = 𝑛
5
𝑛3
10. 𝑎𝑛 =
√𝑛5 +3
