Summation Rules

Going to be dealing with a lot of sums, so knowing the rules of factorizing and expanding is useful

rule 1
$$\sum{X+Y+Z}=\sum_X sigma Y + sigma Z$$

rule 2
constant can be factored out of sigma clause

rule 3
sum of a constant taken N time is

\sigma_{c} = Nc

rule 4
sigma_{X_i+c} = sigma_{X}+Nc

rule 5
sigma_{X_i-c} = sigma_{X}-Nc