Difference between revisions of "User:Temperal/The Problem Solver's Resource8"
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===Diverging-Converging Theorem=== | ===Diverging-Converging Theorem=== | ||
− | A series <math>\ | + | A series <math>\sum_{i=0}^{\infty}S_i</math> converges iff <math>\lim S_i=0</math>. |
===Errata=== | ===Errata=== |
Revision as of 10:59, 6 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
I Chebyshev's InequalityGiven real numbers %{\frac{\sum a_ib_i}{n}} \ge {\frac{\sum a_i}{n}}{\frac{\sum b_i}{n}}%. 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 |