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- 14:56, 14 January 2020 (diff | hist) . . (+2,181) . . N 2006 iTest Problems/Problem 19 (Created page with "==Solution== <asy> unitsize(2.5); draw((0,0)--(0,90)--(90,90)--(90,0)--cycle,linewidth(2)); draw((10,0)--(10,90)); draw((20,0)--(20,90)); draw((30,0)--(30,90),linewidth(2));...")
- 14:12, 14 January 2020 (diff | hist) . . (+625) . . N 2006 SMT/Team Problems/Problem 6 (Created page with "==Solution== Rewriting <math> 16^n+4^n+1 </math> as <math>2^{4n}+2^{2n}+1</math> we can set the two given expressions equal to each other. <cmath>\begin{align*} \frac{(2^{p(...") (current)
- 13:59, 14 January 2020 (diff | hist) . . (+1,084) . . N 2006 SMT/Team Problems/Problem 8 (Created page with "==Solution== To begin, let's rewrite the sum as <cmath>\lim_{n\to\infty} \sum_{k=n^2}^{(n+1)^2} \frac{1}{\sqrt{k}} = \lim_{n\to\infty} \sum_{k=0}^{2n+1} \frac{1}{\sqrt{n^2+...")
- 13:43, 14 January 2020 (diff | hist) . . (+1,220) . . N 2006 SMT/Team Problems/Problem 13 (Created page with "==Solution== A line that passes through the origin has an equation of <math>y=mx</math>. If the line <math>y=mx</math> is tangent to the hyperbola than the equation <math>(mx...")
- 13:26, 14 January 2020 (diff | hist) . . (+2,599) . . N 2006 SMT/Team Problems/Problem 15 (Created page with "==Solution== Denote <math>\prod_{i=0}^{\infty} \frac{c_i^{2}}{c_i^{2}-1}</math> as <math>\prod_{composite} \frac{c^2}{c^2-1}</math>. To begin, let <math>S</math> = <math>\pro...")
- 18:36, 13 January 2020 (diff | hist) . . (+544) . . N 2006 SMT/General Problems/Problem 14 (Created page with "==Solution== Noticing that the first equation, <math>x^2+y^2\le\pi^2</math> is the equation of a disk of radius <math>\pi</math>, and that the graph of <math>y = sin(x)</math...") (current)
- 18:20, 13 January 2020 (diff | hist) . . (+245) . . N 2006 SMT/General Problems/Problem 13 (Created page with "==Solution== This solution does require quite a bit of guessing and testing, but if we notice that we want the numbers to be relatively close so that no term "dominates" the...")
- 18:10, 13 January 2020 (diff | hist) . . (+9) . . m 2006 SMT/General Problems/Problem 10 (→Solution)
- 18:10, 13 January 2020 (diff | hist) . . (+9) . . m 2006 SMT/General Problems/Problem 10 (→Solution)
- 18:09, 13 January 2020 (diff | hist) . . (+58) . . 2006 SMT/General Problems/Problem 10 (→Solution)
- 18:06, 13 January 2020 (diff | hist) . . (+2) . . m 2006 SMT/General Problems/Problem 10 (→Solution)
- 18:06, 13 January 2020 (diff | hist) . . (+15) . . 2006 SMT/General Problems/Problem 10 (→Solution)
- 18:06, 13 January 2020 (diff | hist) . . (+316) . . 2006 SMT/General Problems/Problem 10 (→Solution)
- 17:59, 13 January 2020 (diff | hist) . . (-567) . . 2006 SMT/General Problems/Problem 10 (→Solution) (Tag: Replaced)
- 17:58, 13 January 2020 (diff | hist) . . (+579) . . N 2006 SMT/General Problems/Problem 10 (Created page with "==Solution== First of all, lets note that the sum of all positive integers from <math>1</math> to <math>n</math> inclusive is <math>\frac{n(n+1)}{2}</math>. The sum of all nu...")
- 17:42, 13 January 2020 (diff | hist) . . (+1,227) . . N 2006 SMT/General Problems/Problem 8 (Created page with "==Solution== Assuming all the numbers are positive, lets denote the five numbers as <math>a_0,a_1,a_2,a_3,a_4</math>. Assume WLOG that <math>a_0 \ge a_1 \ge a_2 \ge a_3 \ge a...")
- 16:55, 13 January 2020 (diff | hist) . . (+754) . . N 2013 PMWC Problems/Problem I15 (Created page with "==Solution== First of all, note that <math>M=\sum_{n=1}^\infty \frac{1}{k^2}</math>, and that <math>K=\sum_{n=1}^\infty \frac{1}{(2k-1)^2}</math> Splitting <math>M</math> in...") (current)
- 16:02, 13 January 2020 (diff | hist) . . (+2,801) . . N 2006 iTest Problems/Problem 37 (Created page with "==Solution== To begin, let's number the equations as follows <cmath>\begin{align} x^2 + xy + y^2 &= 1 \\ y^2 + yz +z^2 &= 2 \\ z^2 + zx +x^2 &= 3 \end{align}</cmath> In or...")
- 16:02, 13 January 2020 (diff | hist) . . (-2,802) . . 2006 iTest Problems (→Solution)
- 16:01, 13 January 2020 (diff | hist) . . (+2,803) . . 2006 iTest Problems (→Problem 37)
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