2023 SSMO Relay Round 1 Problems: Difference between revisions
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==Problem 2== | ==Problem 2== | ||
Let <math>T=TNYWR</math>. Let <math>a_0 = 3, a_1 = 1, a_2 = | Let <math>T=TNYWR</math>. Let <math>a_0 = 3, a_1 = 1, a_2 = T</math>, and let <math>a_n = a_{n-1} - \frac{a_{n-3}}{8}</math> for <math>n \ge3.</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]] | ||
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Let <math>T=TNYWR</math>. Find the number of solutions to the equation | Let <math>T=TNYWR</math>. Find the number of solutions to the equation | ||
<cmath>\sec^{ | <cmath>\sec^{T} (Tx) - \tan^{T}(Tx) = 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 
for 
Find ![\[\sum_{i=0}^\infty a_i.\]](http://latex.artofproblemsolving.com/4/9/d/49d916ca4e9ac73751ff00a7a75776bd2eaca943.png)
![\[\sec^{T} (Tx) - \tan^{T}(Tx) = 1\]](http://latex.artofproblemsolving.com/5/e/d/5ed50f1e674d74b015125e05c7737794c09c34a1.png)
such 
