- Mathematical Induction
- By Contradiction
- By Contrapositive
Algebraic
- You can split summations (even infinite ones)
- Equivalently, Pushing log thru product makes it a sum
- Telescoping sums and products
- Break up summations
- Summation of Squared
Probability
- Tower property
- Linearity of expectation. You can switch expectation and summation
- Definition of expectation is an integral (or summation)
Calculus
- switch integrals
Inequalities
- Sum greater than max
- Max greater than averages
- Average greater than min. Combined:
always.