Summation rules

Summary

  • Summation rule 1: The sum of a constant

\[\sum_{i=1}^{n}{ c }=nc\]

  • Summation rule 2: Homogeneity

\[\sum_{i=1}^{n}{ cx_i }=c\sum_{i=1}^{n}{ x_i }\]

  • Summation rule 3: Additivity

\[\sum_{i=1}^{n}{ \left( x_i+y_i \right) }=\sum_{i=1}^{n}{ x_i }+\sum_{i=1}^{n}{ y_i }\]

  • Summation rule 4: Breaking up a sum ( \(1<m<n)\)

\[\sum_{i=1}^{n}{ x_i }=\sum_{i=1}^{m}{ x_i }+\sum_{i=m+1}^{n}{ x_i }\]