Evaluate the infinite geometric series: $$1-\frac{2}{7}+\frac{4}{49}-\frac{8}{343}+\dots$$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Evaluate the infinite geometric series: $$1-\frac{2}{7}+\frac{4}{49}-\frac{8}{343}+\dots$$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{7}{9}
Evaluate the infinite geometric series: $$1-\frac{2}{7}+\frac{4}{49}-\frac{8}{343}+\dots$$
train