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Summation Calculator

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What is Summation?

The Sum of series or Summation of sequences can be defined as adding up the set of values/numbers in an ordered form or series. Summation of sequences has two types of sequences known as finite and infinite set of sequences.

The finite sequence will have an upper limit and lower limit (first and last values) and the infinite sequences will infinitely continue in the series.

Summation properties sequence and arithmetic sequence are different concepts. If you want to learn about arithmetic sequence, try Arithmetic Sequence Calculator.

Summation Notation with Examples:

The meaning of Summation (Σ) is just to "add up". For example, let's say that you had 4 items in a data set: 1,2,5,7 you can think that these values are placed on the x-axis also called x-values. If you were asked to add up all of the items in summation notation, you would see that the:

Summation Calculator

When we are using summation properties, X1 means "the first x-value", X2 means "the second x-value" and so on till the end. For example, let's say that you had a list of weights: 50kg, 100kg, 150kg and 200kg. The weights and their corresponding x-values are:

X1: 50kg
X2: 100kg
X3: 150kg
X4: 200kg

Here is the simple form of Summation Σ(x):

Summation Notation

The "i=1" at the base of Σ means that it is the start of your first x-value. This would be X1 (50kg as shown in the above example). The "n" at the top of Σ means that the end number of the given values”.

In statistics, n is the number of items in the given data set. So, what this summation is asking you to do is “sum up all of your x-values from the first(“i=1”) to the last (n).” For this set of data, that would be:

Summation Example

If you want to learn scientific notation and their role in mathematics, find our Scientific Notation Calculator.

What is Sigma Notation?

The Sigma notation is appearing as the symbol S, which is derived from the Greek upper-case letter, S. The sigma symbol (S) indicate us to sum the values of a sequence. A typical value of the sequence which is going to be add up appears to the right of the sigma symbol and sigma math.

The variable of sigma notation is the variable which is going to add up.

The variable of sigma notation is represented by an index which is placed below the sigma symbol. The index is typically represented by i. (j and t are the other common possibilities for representation of the index in sigma notation).

The index appears in the form of expression simplifier i = 1. The index assumes that values of the sequence starting with the value on the right-hand side of the equation and ending with the value above the sigma notation.

  • The starting point for the summation notation is known as lower limit of summation notation.
  • The stopping point for the summation notation is known as upper limit of summation notation.

For deep learning of limits, try our Limit Calculator for free.

How to calculate Sigma Notation?

To calculate Sigma notation or summation notation we must have these things:

  • Sigma symbol
  • Upper limits
  • Lower limits
  • N number (what to sum)
  • Sequence of value

Example:

what is summation

We have 4 values:

  • X=10
  • X=20
  • X=30
  • X=40

BY using the above equation, we can calculate the summation notation.

How to find summation

After adding up all the values we got summation notation. If you intend to calculate standard deviation and learn, get help from Standard Deviation Calculator.

How to use Summation Notation Calculator?

Sigma notation calculator is an expression simplifier. Our summation notation calculator with variables is very simple and easy to use.

How to use Summation Calculator

To calculate summation notation and summation properties, You have to enter three values into sigma notation calculator

  • Upper limit
  • Function
  • Lower limit

After you entered the values then press "CALCULATE" button and Summation Calculator will calculate the summation of the sequence.

Follow this example to learn, how to use summation notation calculator.

Summation Calculator

After entered the corresponding values:

  • Upper limit =5
  • Function = 4x
  • Lower limit=1

Press "CALCULATE" button and Summation Calculator will calculate the summation of the sequence on the right side of the Summation Calculator in the status block.

For learning & practice of students and teachers, we have other useful calculators like Integral Calculator & Derivative Calculator. You can use them for your advance learning.

We hope our sigma notation calculator helped you to calculate your equation. Please give us your feedback so we could improve it further.


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