User:Temperal/The Problem Solver's Resource3

The Problem Solver's Resource

Introduction \| Other Tips and Tricks \| Methods of Proof \| You are currently viewing page 3.

Summations and Products

Summations: $\sum_{i=a}^{b}c_i=c_a+c_{a+1}+c_{a+2}...+c_{b-1}+c_{b}$
Products: $\prod_{i=a}^{b}c_i=c_a\cdot c_{a+1}\cdot c_{a+2}...c\dot c_{b-1}\cdot c_{b}$

$\sum_{i=a}^{b}x+y=\sum_{i=a}^{b}x+\sum_{i=a}^{b}y$

$\sum_{i=a}^{b}x\cdot y=x\cdot \sum_{i=a}^{b}y=y\cdot \sum_{i=a}^{b}x$

$\prod_{i=a}^{b}x+y+....+z=(x+y+....z)^(b-a+1)$

$\prod_{i=a}^{b}x\cdot y=x^(b-a+1)y^(b-a+1)$