Difference between revisions of "User:DanielL2000"
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3. Compute <cmath>\sum_{a_1=0}^\infty\sum_{a_2=0}^\infty\cdots\sum_{a_7=0}^\infty\dfrac{a_1+a_2+\cdots+a_7}{3^{a_1+a_2+\cdots+a_7}}.</cmath> ''(Harvard-MIT Math Tournament)'' | 3. Compute <cmath>\sum_{a_1=0}^\infty\sum_{a_2=0}^\infty\cdots\sum_{a_7=0}^\infty\dfrac{a_1+a_2+\cdots+a_7}{3^{a_1+a_2+\cdots+a_7}}.</cmath> ''(Harvard-MIT Math Tournament)'' | ||
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+ | Let <math>x,y,z</math> be positive real numbers such that <math> xy+yz+zx\geq3 </math>. Prove that<math> \frac{x}{\sqrt{4x+5y}}+\frac{y}{\sqrt{4y+5z}}+\frac{z}{\sqrt{4z+5x}}\geq1 </math> | ||
== Online Math Circle == | == Online Math Circle == |
Latest revision as of 16:18, 22 February 2014
The home of DL2000
Problems
1. Find all positive integer solutions of the equation $3^x \plus{} 4^y \equal{} 5^z.$ (Error compiling LaTeX. Unknown error_msg) (IMO Shortlist 1991)
2. Find the number of integers such that (Harvard-MIT Math Tournament)
3. Compute (Harvard-MIT Math Tournament)
4. Let be positive real numbers such that . Prove that
Online Math Circle
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