2020 CIME I Problems/Problem 7
Problem 7
For every positive integer 
, define ![\[f(n)=\frac{n}{1 \cdot 3 \cdot 5 \cdots (2n+1)}.\]](http://latex.artofproblemsolving.com/4/e/6/4e66db1ce558cf1817f1579286937d4ed44e956b.png)
Suppose that the sum 
can be expressed as 
for relatively prime integers 
and 
. Find the remainder when is divided by 
.
Solution
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