\frac{1}{100}
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Express the value of the following as a common fraction:
$\left(1-\frac12\right)\cdot\left(1-\frac13\right)\cdot\left(1-\frac14\right) \dotsm \left(1-\frac1{n+1}\right) \dotsm \left(1-\frac1{100}\right)$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{100}
Express the value of the following as a common fraction:
$\left(1-\frac12\right)\cdot\left(1-\frac13\right)\cdot\left(1-\frac14\right) \dotsm \left(1-\frac1{n+1}\right) \dotsm \left(1-\frac1{100}\right)$
train