Summation Rules

Here is a list of summation rules, with 'k' denoting a constant:

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


2. \[\sum_{i=1}^{n}{(x_i - y_i)} = \sum_{i=1}^{n}{x_i}  - \sum_{i=1}^{n}{y_i}\]


3. \[\sum_{i=1}^{n}{x_iy_i} \neq \sum_{i=1}^{n}{x_i} \times \sum_{i=1}^{n}{y_i}\]


4. \[\sum_{i=1}^{n}{x_i}^2 \neq (\sum_{i=1}^{n}{x_i})^2\]


5. \[\sum_{i=1}^{n}{k} = nk\]


6. \[\sum_{i=1}^n{(x_i + k)} = \sum_{i=1}^{n}{x_i} + \sum_{i=1}^{n}{k} = \sum_{i=1}^{n}{x_i}+nk\]


7. \[\sum_{i=1}^{n}{(x_i-k)} = \sum_{i=1}^{n}{x_i} - nk\]