Infinite Series Calculator
A series is defined as the sum of a given sequence. The sum of a particular part of a sequence is called its partial sum.
What is Infinite Series Calculator?
'Infinite Series Calculator' is an online tool that helps to calculate the summation of infinite series for a given function. Online Infinite Series Calculator helps you to calculate the summation of infinite series for a given function in a few seconds.
Infinite Series Calculator
How to Use Infinite Series Calculator?
Please follow the steps below on how to use the calculator:
- Step 1: Enter the function in the given input box.
- Step 2: Click on the "Find" button to find the summation of the infinite series
- Step 3: Click on the "Reset" button to clear the fields and enter a new function.
How to Find Infinite Series Calculator?
The summation is defined as the addition of a large number of data that are a concerned sequence of any kind of numbers, called addends or summands. ∑ the symbol is used for a total sum which is called sigma to denote summation.
The sum of the infinite series of an arithmetic series is undefined.
The sum to infinity for a geometric series is undefined when |r| > 1, where 'r' is the common ratio.
The sum to infinity for a geometric series is \({S_\infty } = \frac{a}{1-r}\) when |r| < 1 and 'a' is the first term.
Solved Examples on Infinite Series Calculator
Example 1:
Find sum of infinite series for a function \(\sum_{x =1}^{∞} \frac{5}{2^x}\)
Solution:
x = 1, first term a = 5 / 2
= 5
common ratio r = (5/2)/(5/4)
= 1/2
\({S_\infty } = \frac{a}{1-r} = \frac{\frac{5}{2}}{{1 - \frac{1}{2}}}\)
= 5
Similarly, you can try the calculator to infinite series for the following functions:
- \(\sum_{x =1}^{∞} \frac{3}{2^x}\)
- \(\sum_{x = 0}^{∞} \frac{5}{3^x}\)