009C Sample Final 2, Problem 1

Test if the following sequences converge or diverge. Also find the limit of each convergent sequence.

a) $a_{n}={\frac {\ln(n)}{\ln(n+1)}}$

b) $a_{n}={\bigg (}{\frac {n}{n+1}}{\bigg )}^{n}$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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