Compute
\[\sum_{1 \le j < i} \frac{1}{2^{i + j}},\]where the sum is taken over all positive integers $i$ and $j$ such that $1 \le j < i.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute
\[\sum_{1 \le j < i} \frac{1}{2^{i + j}},\]where the sum is taken over all positive integers $i$ and $j$ such that $1 \le j < i.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{3}
Compute
\[\sum_{1 \le j < i} \frac{1}{2^{i + j}},\]where the sum is taken over all positive integers $i$ and $j$ such that $1 \le j < i.$
train