Difference between revisions of "User:Temperal/The Problem Solver's Resource3"

Revision as of 17:46, 29 September 2007

The Problem Solver's Resource

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

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

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

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

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

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

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 | style="background:lime; border:1px solid black;height:200px;padding:10px;" | {{User:Temperal/testtemplate|page 3}}
 ==<span style="font-size:20px; color: blue;">Summations and Products</span>==
-<!-- will fill in soon, if someone else could in the meantime, it would be appreciated. -->
+===Definitions===
+*Summations: <math>\sum_{i=a}^{b}c_i=c_a+c_{a+1}+c_{a+2}...+c_{b-1}+c_{b}</math>
+*Products: <math>\prod_{i=a}^{b}c_i=c_a\cdot c_{a+1}\cdot c_{a+2}...c\dot c_{b-1}\cdot c_{b}</math>
+===Rules of Summation===
+<math>\sum_{i=a}^{b}x+y=\sum_{i=a}^{b}x+\sum_{i=a}^{b}y</math>
+<math>\sum_{i=a}^{b}x\cdot y=x\cdot \sum_{i=a}^{b}y=y\cdot \sum_{i=a}^{b}x</math>
+<!--there are others, I forgot what they were. Could someone please fill them in? -->
+===Rules of Products===
+<math>\prod_{i=a}^{b}x+y+....+z=(x+y+....z)^(b-a+1)</math>
+<math>\prod_{i=a}^{b}x\cdot y=x^(b-a+1)y^(b-a+1)</math>
+<!-- same as above, there are others.... but no fancy ones like divergence/convergence, please -->
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 |} <br /><br />