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