Which of the following sequences ( a n ) n ≥ 1 {\displaystyle (a_{n})_{n\geq 1}} converges? Which diverges? Give reasons for your answers!
(a) a n = ( 1 + 1 2 n ) n {\displaystyle a_{n}={\bigg (}1+{\frac {1}{2n}}{\bigg )}^{n}}
(b) a n = cos ( n π ) ( 1 + n n ) n {\displaystyle a_{n}=\cos(n\pi ){\bigg (}{\frac {1+n}{n}}{\bigg )}^{n}}
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