Subscript and Summation Notation Single Subscript ... - Statpower

The Algebra of SummationsMany facts about the way lists of numbersbehave can be derived using some basicrules of summation algebra. These rules aresimple yet powerful.• The first constant rule• The second constant rule• The distributive ruleThe First Constant RuleThe first rule is based on a fact that you firstlearned when you were around 8 years old:multiplication is simply repeated addition.That is, to compute 3 times 5, you compute5+5+5.Another way of viewing this fact is that, if youadd a constant a certain number of times, you havemultiplied the constant by the number of times itwas added.The First Constant RuleSymbolically, we can express the rule as:The First Constant Rule(Simplified Version)Symbolically, we can express the rule as:y∑a = ( y− x+1) aN∑a=Nai=xi=1