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May 12, 2015



Finding the Sum of a Series Using Sigma Notation


Posted: May 1st, 2015  
In math a sequence is a function that has a set of natural numbers as its domain. Natural numbers are all positive integers above zero, not including zero. Some examples are 1, 34, 245. Take the following sequence for example. "n" is used for the variable as a reminder that this function is a sequence and n must be a natural number. If you added up 25, 30, 35, 40, 45 and 50, you would find the sum of all the values between n=3 and n= 7, is 175.
You could write the exact same problem using summation notation. To solve the problem using Sigma notation, you must be familiar with the Summation Properties and Rules. First you would use property 3 to separate the terms of the function (called a sequence) into two different groups like this.
Then you would use property 2 to separate the variable from the constant in the first term like so.
For the first term in this expression, you must use rule 1 to replace in 5n+10 with
This first term in the expression simplifies to: From here, you multiply 28 by 5 which equals 140 and the first term in the expression further simplifies to 140. For the second term in the expression you will use the property 1 which is the constant property. Using summation property 1 on the second term you will multiply 7 by 10 which equals 70. And the second term further simplifies to 70. Your expression now looks like140 + 70 = 210 However that is not the solution. There is still one more step. Because we want to find the sum of values between 3 and 7 we must subtract the Therefore subtracting 35 from 210 gives the correct answer of 175.
by Andrea Boggs Reference list Horsnby, Lial, Rockwold (2011) A Graphical Approach to College Algebra. 5th ed. Addison Wesley. 
