Question

for the following sequence {a^n}n>=1, find limn->infinity a^n or state why it does not exist:

Answer 1

\[1. a _{n} = \log(n) - \log(n+1)\]

Answer 2

2. \[a _{n} = \log(e+e ^{n}) \div 3n\]

Answer 3

3. \[a _{n} = n!/n ^{n}\]

Answer 4

4. \[a _{n} = (e ^{n}-e ^{-n})/(e ^{n}+e ^{-n})\]

Answer 5

5. \[a _{n} = \sin^{-1} ((1-n ^{-1})^{3}) + \cos^{-1} ((1-n ^{-1})^{3})\]

Answer 6

6. \[a _{n} = e ^{-n ^{2}} \int\limits_{0}^{n} e ^{t ^{2}}\]

Answer 7

7. \[a _{n} = [\log(n)]^{\log(1-n ^{-1})}\]