Difference between revisions of "User:Temperal/The Problem Solver's Resource8"
(I think the Power mean inequality is the same thing as the general mean inequality (at least, their descriptions here are)) |
(okay. I like the name power mean better, though. :)) |
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This will also cover diverging and converging series, and other such calculus-related topics. | This will also cover diverging and converging series, and other such calculus-related topics. | ||
− | === | + | ===Power Mean Inequality=== |
Take a set of functions <math>m_j(a) = \left({\frac{\sum a_i^j}{n}}\right)^{1/j}</math>. | Take a set of functions <math>m_j(a) = \left({\frac{\sum a_i^j}{n}}\right)^{1/j}</math>. |
Revision as of 17:48, 9 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
Minkowsky'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 |