If $k = \frac{1}{1+2x}$, where $x$ is an integer greater than $1$ and $k$ can be represented as a terminating decimal, find the sum of all possible values of $k$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $k = \frac{1}{1+2x}$, where $x$ is an integer greater than $1$ and $k$ can be represented as a terminating decimal, find the sum of all possible values of $k$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{4}
If $k = \frac{1}{1+2x}$, where $x$ is an integer greater than $1$ and $k$ can be represented as a terminating decimal, find the sum of all possible values of $k$.
train