subject: Importance Of Sigma Notation [print this page] What is Sigma Notation? What is Sigma Notation?
Sigma notation is the summation method that presents long sum in precise way. The sigma notation is commonly termed as summation or sum up and it is represented using the symbol. The sigma will be associated with a variable and the range of values that have to be specified for that variable or a separate range variable.
How to Solve Sigma Notation?
The sigma notation will be associated with a function containing a variable and the variable will be supplied with a range of values. The sigma notation solver is a simple and straight forward summation strategy that works with simple sigma notation formula. The sigma notation formula and the way to solve it are demonstrated using the following sigma notation examples.
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Example 1:
If the function is sigma of a where a varies from 1 to 6, then the variable a will be supplied with the values 1 through 6 and these 6 numbers will be added together. Thus, the sigma of a (with a varying from 1 to 6) will be equivalent to addition of 1, 2, 3, 4, 5, 6 and the result will be 21. This is illustrated below:
6 sigma (a=1) [a] = 1+2+3+4+5+6 = 21
Example 2:
In the above function, we used only the variable a as the expression or function of summation. Instead, we can find the summation of any complicated function using this sigma notation. For example, if you have to sum up the values for the expression (2a+1) where a ranges from 1 to 3, then you have to supply the values 1, 2, and 3 one at a time to the expression (2a+1), compute the resultant value while applying each value and then sum up the resultant values. Thus sigma of (2a+1) where a ranging from How to Solve Sigma Notation 1 to 3 will be (2 x 1 + 1) + (2 x 2 + 1) + (2 x 3 + 1), which can be simplified as (2+1) + (4+1) + (6+1). This equation can further be reduced into 3 + 5 + 7 resulting in 15.
The above example is shown below in the form of mathematical equations:
3sigma (a=1) [2a+1] = (2 x 1 + 1) + (2 x2 +1) + (2 x 3 +1)
= (2+1) + (4+1) + (6+1)
= 3 + 5 + 7 = 15
Sigma Notation Rules
There are many sigma notation rules that help you solve the sigma equations easily and efficiently. Given below are two common rules among them:
Rule 1: Summation of a where the range variable i varies from 1 to n is done by adding a for n number of times. This is equivalent to multiplying a by n.
Rule 2: Summation of a where a ranges from 1 to k is computed by adding 1, 2, 3, , k. This is equivalent to performing the computation (k x (k+1))/2.
