Difference between revisions of "User:Temperal/The Problem Solver's Resource8"
(okay. I like the name power mean better, though. :)) |
(→Minkowsky's Inequality: i) |
||
Line 26: | Line 26: | ||
<math>{\frac{\sum a_ib_i}{n}} \ge {\frac{\sum a_i}{n}}{\frac{\sum b_i}{n}}</math>. | <math>{\frac{\sum a_ib_i}{n}} \ge {\frac{\sum a_i}{n}}{\frac{\sum b_i}{n}}</math>. | ||
− | === | + | ===Minkowski's Inequality=== |
Given real numbers <math>a_1,a_2,...,a_n</math> and <math>b_1,b_2,\ldots,b_n</math>, the following holds: | Given real numbers <math>a_1,a_2,...,a_n</math> and <math>b_1,b_2,\ldots,b_n</math>, the following holds: |
Revision as of 15:16, 26 October 2007
Intermediate Number TheoryThese are more complex number theory theorems that may turn up on the USAMO or Pre-Olympiad tests. This will also cover diverging and converging series, and other such calculus-related topics. Power Mean InequalityTake a set of functions Note that
, if Chebyshev's InequalityGiven real numbers
Minkowski's InequalityGiven real numbers
Nesbitt's InequalityFor all positive real numbers
Schur's inequalityGiven positive real numbers
Fermat-Euler IdentitityIf Gauss's TheoremIf Diverging-Converging TheoremA series ErrataAll quadratic residues are |