009C Sample Final 3, Problem 1

Which of the following sequences $(a_{n})_{n\geq 1}$ converges? Which diverges? Give reasons for your answers!

a)  $a_{n}={\bigg (}1+{\frac {1}{2n}}{\bigg )}^{n}$

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

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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