Subscript and Summation Notation Single Subscript ... - Statpower

The Second Constant RuleThe rule states thatN∑ii= 1 i=1Again, the rule appears to be saying less than itactually is. At first glance, it appears to be a ruleabout multiplication. You can move a factorableconstant outside of a summation operator.However, the term a could also stand for afraction, and so the rule also applies to factorabledivisors in the summation expression.N∑aX = a XiThe Second Constant Rule(Examples)Apply the Second Constant Rule to thefollowing:N∑i=16yXXNii=1 2∑iThe Distributive Rule ofSummation AlgebraThe third rule of summation algebra relatesto a another fact that we learned early in ourmathematics education --- when numbersare added or subtracted, the ordering ofaddition and/or subtraction doesn't matter.For example(1 + 2) + (3 + 4) = (1 + 2 + 3 + 4)The Distributive Rule ofSummation AlgebraSo, in summation notation, we haveN N N∑( + ) = ∑ + ∑X Y X Yi i i ii= 1 i= 1 i=1Since either term could be negative, we alsohaveN N N∑( − ) = ∑ −∑X Y X Yi i i ii= 1 i= 1 i=1