What is a Summation & How do you Solve it?


A summation is the process of summing many terms altogether which are terms as addends. Sigma notation is a common technique to write summations. The summation is represented by a Σ (capital sigma) symbol and represents the summation of a sequence. 

The Σ is used to represent sequence as well as the series in arithmetic. The following is a summation of the sequence of three numbers, for example.

This signifies the summation of sequence of numbers is represented by the i + 1 which starts from i = 0 to i = 4. The sequence element is computed at each step by replacing the current i value in the expression. Sigma notation calculator with steps helps us to calculate this online.

Types of Summation

The summation can be of two different types the infinite summation and the finite summation. The finite sequence has the upper and lower limits i.e. a starting and an ending value whereas the infinite sequences will continue in series infinitely i.e. comprising infinite numbers. 

What is Sigma

Sigma is a Greek letter which can be represented in capital form as Σ and in lower case as σ. It is the eighteenth letter in Greek alphabets which corresponds to letter S in English. As the S stands for sigma the letter Σ will use. 

To represent the summation however, the capital sigma letter will use i.e. Σ. In summation the sigma is usually accompanied by an index and two bounds known as upper and lower limits of summation.

Sigma/Summation Notation

Sigma notation provides a concise approach for a large number of sums and has often used in the arithmetic or geometric series process. The symbol Σ (sigma) means a sum has calculated for the following values. The variable k refers to the sum index. The numbers at the upper and lower ends of the Σ are referring to as upper and lower limit of summation respectively.

The upper bound or limit in this situation is 7 and the lower limit is 4. The notation implies that every integer value k takes from 4 to 7 (thus 4, 5, 6, 7) and plugs each of them into the summand formula (here that formula is 3k). Then all of them will sum up altogether.

Related: Summation also helps to find the average of the number. Since summation is the sum of all numbers. So if we divide the sum by the number of terms it provides us an average of the number that we may calculate by an average finder.

How to Calculate Summation

For a series of expressions as well as numbers addition, the Summation Notation has utilized. For instance, the expression 4n + 2 using summation notation will represent as: 

In the expression above, n is the integer placeholder, and we add 4n + 2 along with integers from 2 to 6.

We know we are going to sequence from 2, 3, 4, 5 and 6 since the lower limit is 2 and the upper bound is 6. We’ll add 2 into the expression, and then add 3 into the expression and add 4 in the expression and so on, till our ultimate integer of 6 comes while adding up.

Instead of n various variables may substitute including i, j or x. In order to utilize alternative integer placeholders, replace n with the new integer placeholders in the formula of summation.

Why we use Sigma Notation

You can simplify the representation of addition by using the sigma notation. You can simply write them like this “Σ” in a perfect sigma notation instead of all the elements being written like this i.e. a1 + a2 + a3 + a4 + a5 + a6. Moreover, you can algebraically manipulate the sums without even having to spread all the sums by utilizing the sigma notation. 

As we have learned from the summation, however, a summation may use to sum up a mathematical expression. This expression consists of several numbers that we add in a simple and conciseness. Furthermore, the area under a curve may determine using the summation notation, as the integration includes a summation concept.

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