Let $a_0 = 6$ and
\[a_n = \frac{a_{n - 1}}{1 + a_{n - 1}}\]for all $n \ge 1.$  Find $a_{100}.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a_0 = 6$ and
\[a_n = \frac{a_{n - 1}}{1 + a_{n - 1}}\]for all $n \ge 1.$  Find $a_{100}.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{6}{601}
Let $a_0 = 6$ and
\[a_n = \frac{a_{n - 1}}{1 + a_{n - 1}}\]for all $n \ge 1.$  Find $a_{100}.$
train