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 ( $1<m<n)$

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