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       Dragon Hellfire
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   DIR Return to: Mathematics - General
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       #Post#: 106--------------------------------------------------
       Proof Techniques
   DIR By: Dragon Hellfire
       Date: May 15, 2019, 1:51 am
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       Introductory
       Fundamental Methods
       - Direct Proof
       - Proof by Contradiction
       - Proof by Contraposition
       - Proof by Induction
       Calculus
       Sums and Seires: Divergence and Convergence
       -> Theorems
       - Theorem 1 The harmonic series is divergent
  HTML https://web.williams.edu/Mathematics/lg5/harmonic.pdf
       - Theorem 2 The geometric series is conditionally convergent.
  HTML http://mathfaculty.fullerton.edu/mathews/c2003/complexgeometricseries/ComplexGeometricSeriesTheorem.1.pdf
       - Theorem 3 Absolute convergence implies convergence.
       ->Tests
       - Direct Comparison (If a smaller sum diverges, sum diverges ;;
       if a greater sum converges, sum converges)
       - Integral Test (If itegral converges, sum converges)
       - Limit Comparison Test (If limit does not approach zero, sum
       diverges)
       - Root Test
       - Ratio Test (If absolute value of the ratio of (n+1)th term and
       the reciprocal of the nth term is less than 1, sum converges)
       -->Useful Skills
       - Partial Fraction Decomposition
       -
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