# Series Calculator

Series Calculator helps to calculate the sum of the specified sequence between a given interval. A series is obtained when all the elements of a sequence are added. Sequences and series are basic mathematical concepts.

## What is Series Calculator?

Series Calculator is an online tool that helps to calculate the value of the series after adding all the elements of a sequence represented by a general function. Arithmetic series, Geometric series, and Harmonic series are different types of mathematical series. To use the **series calculator**, enter the values in the given input boxes.

### Series Calculator

**NOTE: **Enter the function in terms of x only.

## How to Use Series Calculator?

Please follow the steps below to find the value of the series using the online series calculator:

**Step 1:**Go to online series calculator.**Step 2:**Enter the values in the given input boxes.**Step 3:**Click on the**"Find"**button to find the value of the series.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Series Calculator Work?

When numbers are grouped together according to some specific rules it results in a sequence. When we take the summation of all the numbers in a sequence it gives us a series. The order of elements or the pattern of numbers in a series does not matter. Given below are the three most commonly used sequences and series.

**Arithmetic series**- when the successive terms in a sequence differ from each other by a fixed amount it is known as an arithmetic sequence. By taking the sum of an arithmetic sequence we get an arithmetic series.**Geometric series**- when the consecutive terms in a sequence have a common ratio it is known as a geometric sequence. A series formed from a geometric sequence is known as a geometric series.**Harmonic series**- when we take the reciprocal of the terms in an arithmetic sequence it forms a harmonic sequence. A harmonic sequence is used to form a harmonic series.

Suppose we are given a function, f(x), and we want to find the value of this series from x = 0 to x = n. The following steps can be used:

- Find the value of the function at x = 0, x = 1, x = 2 ... x = n.
- Add these values f(0) + f(1) + f(2) .... + f(n). This summation will give the value of the series.

## Solved Examples on Series Calculator

**Example 1:**

Find the value of the series for f(x) = x + 5, from x = 0 to x = 5. Verify the result using the online series calculator.

**Solution:**

\(\sum_{0}^{5}x + 5\)

= (0 + 5) + (1 + 5) + (2 + 5) + ( 3 + 5) + (4 + 5) + (5 + 5)

= 5 + 6 + 7 + 8 + 9 + 10

= 45

Therefore, the value of \(\sum_{0}^{5}x + 5\) is 45

**Example 2:**

Find the value of the series for f(x) = x^{3}, from x = 0 to x = 4. Verify the result using the online series calculator.

**Solution:**

\(\sum_{0}^{4}x^{3}\)

= (0)^{3} + (1)^{3} + (2)^{3} + (3)^{3} + (4)^{3}

= 100

Therefore, the value of \(\sum_{0}^{4}x^{3}\) is 100

Similarly, you can try the series calculator to find the value of the series for the following:

- \(\sum_{0}^{6}x^{2} - 1\)
- \(\sum_{0}^{2}\frac{x^{4}}{4}\)

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