Difference between revisions of "2020 CIME I Problems/Problem 7"
(Created page with "==Problem 7== For every positive integer <math>n</math>, define <cmath>f(n)=\frac{n}{1 \cdot 3 \cdot 5 \cdots (2n+1)}.</cmath> Suppose that the sum <math>f(1)+f(2)+\cdots+f(20...") |
|||
| Line 5: | Line 5: | ||
{{solution}} | {{solution}} | ||
| − | {{CIME box|year=2020|n=I|num-b= | + | {{CIME box|year=2020|n=I|num-b=6|num-a=8}} |
[[Category:Intermediate Number Theory Problems]] | [[Category:Intermediate Number Theory Problems]] | ||
{{MAC Notice}} | {{MAC Notice}} | ||
Revision as of 11:27, 31 August 2020
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
This problem needs a solution. If you have a solution for it, please help us out by adding it.
| 2020 CIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All CIME Problems and Solutions | ||
The problems on this page are copyrighted by the MAC's Christmas Mathematics Competitions. 
