Calculating with sigma notation{{CMD_98}} We want to use sigma notation to simplify our calculations. To do that, we will need to know some basic sums. First, let's talk about the sum of a constant. (Notice here, that our upper limit of summation is {{MATH_99}}. {{MATH_100}} is not the index variable, here, but the highest value that the index variable will take.) {{MATH_101}} This is a sum of {{MATH_102}} terms, each of them having a value {{MATH_103}}. That is, we are adding {{MATH_104}} copies of {{MATH_105}}. This sum is just {{MATH_106}}. The other basic sums that we need are much more complicated to derive. Rather than explaining where they come from, we'll just give you a list of the final formulas, that you can use. {{ENV_107}} {{ENV_108}} {{ENV_109}}