May 25, 2021

# Summation Notation

Mathematically, the summation is the method of adding any numbers, such as addends or summands, to produce the sum or addition.

In summation aside from numbers, any value, such as functions, polynomials, matrices, functions, and so on, can be summed up.

In other words, a series is a summation sequence in which the mathematical operation “+” is specified. While the summation notation is the notation or the sign that represents the summation i.e. “Σ”.

“Σ” is a Greek upper case letter known as sigma and it represents the English alphabet “S” which stands for sum. Usually, the sigma sign is used to represent the summation of several multiple terms.

Sigma notation allows you to express any number, that is, a set of items that must be added together, in a compact and precise manner.

## How to Calculate Summation Notation?

Although it may seem a bit tough if you’ve never done a summation notation calculator before, not to worry it’s really very easy.

The summation method is convenient, and it provides a succinct expression for the sum of the values of the variables, which is common in mathematical calculations.

Moreover, to define the definite integral of a continuous function of a variable in a closed interval the summation notation could be implemented.

Generally, the algebraic expression X1+X2+X3+…+XN is used in the formula to calculate the summation notation.

The to be continued dots between the expression represents that some of the values are skip while writing and must be added during calculations.

Since writing an expression like this is risky, mathematicians devised the summation notation, a shorthand notation for representing a sum of scores.

The summation notation is the expression that is represented before the equals sign while the expression after the equals sign is the “longhand” notation.

## Arithmetic Sequence

A sequence of numbers in which every progressive value is the sum of the previous one and a constant “d” is known as arithmetic progression or arithmetic sequence.

In the arithmetic sequence, we can proceed to the next value from the current by always adding or subtracting the current value.

The “common difference” d is what the number added (or subtracted) at each point of an arithmetic sequence is. As you subtract (that is, find the difference of) successive values, you’ll get this common value.

An arithmetic series can be thought of as a feature on the sphere of natural numbers.

The arithmetic sequence is a linear function and its rate of change is constant. Thus the slope of the function, or the constant rate of change, is a common difference. If we know the slope and vertical intercept, we can create the linear function.

## How to Calculate the Arithmetic Sequence?

The sum of all the digits in an arithmetic sequence is calculated using the addition of the arithmetic sequence formula.

While recalling the previous knowledge, the addition of the values is an arithmetic series of finite arithmetic progress. The arithmetic series calculator helps to find the arithmetic value online.

The arithmetic sequence typically follows the following pattern: (a, a + d, a + 2d,…), where “a” is the first value and “d” as we know is a common difference.

Generally, there are two methods to calculate the arithmetic sequence. The following formula could be used to calculate the arithmetic sequence
S = n⁄2 (a + L)
S = n⁄2 {2a + (n − 1) d}

Both the formulas could be used to calculate the sum of the arithmetic sequence, however, we use the former one when the last value is provided in the problem. While the latter one is implemented when the last value is not provided in the query.