Theorems
- \[\sum_{i=1}^n bx_i=b \sum_{i=1}^n x_i\]
- \[\sum_{i=1}^n (ax_i-b)=a \sum_{i=1}^n x_i-nb\]
- \[\sum_{i=1}^n (ax_i^2-bx_i+c)=a\sum_{i=1}^n x_i^2-b\sum_{i=1}^n x_i + nc\]
- \[\sum_{i=1}^n (ax_i-by_i)=a\sum_{i=1}^n x_i - b \sum_{i=1}^n y_i\]
- \[\sum_{i=1}^n (ax_i-b)^2=a^2 \sum_{i=1}^n x_i^2 - 2ab \sum_{i=1}^n x_i + nb^2\]
- \[(\sum_{i=1}^n x_i)^2=\sum_{i=1}^n x_i^2 + \sum_{i \ne j}^n\sum x_ix_j\]
- \[\prod_{i=1}^k x_iy_i = (\prod_{i=1}^k x_i)(\prod_{i=1}^k y_i)\]
- \[\sum_{i=1}^m \sum_{i=1}^n (x_i+y_j)=n\sum_{i=1}^m x_i + m \sum_{i=1}^n y_j\]
- m\(\sum_{i=1}^m \sum_{i=1}^n (x_iy_j)=(\sum_{i=1}^n x_i) (\sum_{i=1}^n y_j)\)