2a. PLEASE WRITE CLEARLY 2. For each of the following **SEQUENCES**, determine whether it converges or diverges. If it converges, find the limit. **(GIVE REASONS FOR YOUR ANSWERS.** Note that the "Tests for Convergence" are for series, **NOT** for these problems.)a. \( a_n = 1 + (0.8)^n \)b. \( a_n = \frac{n}{\ln n} \, (n = 2, 3, 4, \ldots) \)

Name: 2a. PLEASE WRITE CLEARLY 2. For each of the following **SEQUENCES**, d
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: 2a. PLEASE WRITE CLEARLY 2. For each of the following **SEQUENCES**, determine whether it converges or diverges. If it converges, find the limit. **(GIVE REASONS FOR YOUR ANSWERS.** Note that the "Tests for Convergence" are for series, **NOT** for th

2 a) Given: an=1+0.8n. Determine whether the sequence converges or diverges as follows.If limn→∞an exists, the sequence an is convergent and if limn→∞an does not exists or is equal to infinity, then the sequence an is divergent. Now compute the limit limn→∞an as shown below. limn→∞an=limn→∞1+0.8n=limn→∞1+limn→∞0.8n=1+limn→∞0.8n=1+limn→∞eln0.8n Since eln a=a =1+limn→∞enln0.8 Since ln ab=bln a=1+limn→∞e-0.2231n Since ln0.8≈-0.2231=1+e-∞=1+0 Since e-∞=0=1 Here, the limit limn→∞an exists and is finite. Hence, the sequence an converges. And the limit value is 1.