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) = x3, 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:
- \(\sum_{0}^{6}x^{2} - 1\)
- \(\sum_{0}^{2}\frac{x^{4}}{4}\)