Difference between revisions of "User:Temperal/The Problem Solver's Resource8"
m (→Chebyshev's Inequality: typo fix) |
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<math>m_x \le m_y</math> for reals <math>x<y</math>. | <math>m_x \le m_y</math> for reals <math>x<y</math>. | ||
− | + | , if <math>m_2</math> is the quadratic mean, <math>m_1</math> is the arithmetic mean, <math>m_0</math> the geometric mean, and <math>m_{-1}</math> the harmonic mean. | |
===Chebyshev's Inequality=== | ===Chebyshev's Inequality=== |
Revision as of 17:37, 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. General 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 Power Mean InequalityFor a real number
Diverging-Converging TheoremA series ErrataAll quadratic residues are |