Determine the value of the infinite sum
\[\sum_{n = 17}^\infty \frac{\binom{n}{15}}{\binom{n}{17}}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Determine the value of the infinite sum
\[\sum_{n = 17}^\infty \frac{\binom{n}{15}}{\binom{n}{17}}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
272
Determine the value of the infinite sum
\[\sum_{n = 17}^\infty \frac{\binom{n}{15}}{\binom{n}{17}}.\]
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