Summation is the operation of adding a sequence of numbers to get a sum or total. It is usually denoted with the letter sigma (). A sum of all the numbers from 1 to 5 can be written as:
Any operation can be performed on . For instance,
A partial sum, where the sum is only of part of a series, is also called a finite sum. If a sum is between a number and infinity, it is called a series. Infinite sums can be divergent, meaning they approach infinity (such as ), or convergent, meaning they equal a specific value (for instance, ).
A sum of any series in which is multiplied or divided by a constant is the same as the entire sum multiplied or divided by said constant. If is a constant,
If the sequence is of two numbers added to each other, the answer will be the same as the sums of both terms added together.
Sums where is raised to a power can be found with the following formulas:
If a sum is geometric, or in the form
the sum is equal to
If the sum of a geometric series is infinite and convergent (), the formula still applies, but since
we can use the latter formula.