Difference between revisions of "2023 SSMO Relay Round 1 Problems"
| (One intermediate revision by the same user not shown) | |||
| Line 4: | Line 4: | ||
[[2023 SSMO Relay Round 1 Problems/Problem 1|Solution]] | [[2023 SSMO Relay Round 1 Problems/Problem 1|Solution]] | ||
| + | |||
==Problem 2== | ==Problem 2== | ||
| − | Let <math>T=</math> | + | Let <math>T=TNYWR</math>. Let <math>a_0 = 3, a_1 = 1, a_2 = N</math>, and let <math>a_n = a_{n-1} - \frac{a_{n-3}}{8}</math>. Find <cmath>\sum_{i=0}^\infty a_i.</cmath> |
[[2023 SSMO Relay Round 1 Problems/Problem 2|Solution]] | [[2023 SSMO Relay Round 1 Problems/Problem 2|Solution]] | ||
| + | |||
==Problem 3== | ==Problem 3== | ||
| − | Let <math>T=</math> | + | Let <math>T=TNYWR</math>. Find the number of solutions to the equation |
<cmath>\sec^{N} (Nx) - \tan^{N}(Nx) = 1</cmath> | <cmath>\sec^{N} (Nx) - \tan^{N}(Nx) = 1</cmath> | ||
such <math>0 \le x \le \pi</math> | such <math>0 \le x \le \pi</math> | ||
[[2023 SSMO Relay Round 1 Problems/Problem 3|Solution]] | [[2023 SSMO Relay Round 1 Problems/Problem 3|Solution]] | ||
is divided by 
.
. Let 
, and let 
. Find ![\[\sum_{i=0}^\infty a_i.\]](http://latex.artofproblemsolving.com/4/9/d/49d916ca4e9ac73751ff00a7a75776bd2eaca943.png)
![\[\sec^{N} (Nx) - \tan^{N}(Nx) = 1\]](http://latex.artofproblemsolving.com/7/d/4/7d49bb2538173262736562e0aa9be39bf39043cd.png)
such 
