# Infinite Series Calculator

**Created By :** Abhinandan Kumar

**Reviewed By :** Phani Ponnapalli

**Last Updated :** Mar 28, 2023

An infinite sequence calculator is an online tool that helps to calculate the sum of the given function for the given limits. For faster calculations, use our calculator by just giving the inputs in the input fields and getting the concerned output.

### How to Find the Sum of the Infinite Sequences of Function Manually?

Infinite series is the sum of the values in an infinite sequence of numbers. The infinite sequence is represented as (∑) sigma. Now, we will see the standard form of the infinite sequences is

Σ_{0} ^{∞} r^{n}

where

o is the upper limit.

∞ is the lower limit.

r is the function.

The infinite sequence of a function is

**Σ _{0}^{∞} r^{n} = 1/(1-r).**

Now we will look into the steps that are given below to calculate the sum of the infinite sequences of a function easily.

- Take the given function that was given in the problem.
- Convert the given function into the standard form of infinite sequences.
- Apply the infinite sequences of the formula.
- After simplifying it we will get the answer easily.

**Example:**

**Question: Evaluate the sum of Σ _{0}^{∞} 1/5^{n}?**

**Solution:**

Given, Σ_{0}^{∞} 1/5^{n}

r = 1/5

Apply the formula,

Σ_{0}^{∞} r^{n} = 1/(1-r)

Σ_{0}^{∞ }(1/5)^{n} = 1 / ( 1 - (1/5))

= 1 / 0.8

= 1.25.

Stay tuned to our sequencecalculators.com website which has all sequence calculator tools to calculate easily for your assignments.

### FAQs on Infinite Sequence Calculator

**1. How do we use our infinite sequence calculator tool?**

All we need to do is give the inputs in the input fields and click on the calculate button that gives the answers easily.

**2. How to calculate the infinite sequence easily?**

The infinite sequence can be calculated by the formula Σ_{0}^{∞} r^{n} = `1/(1-r)`.

**3. What is the standard form of the infinite sequence?**

A standard form of the infinite sequence is Σ_{0} ^{∞} r^{n}.

**4. Which tool is best to find the infinite sequence?**

The infinite sequence calculator is the best online tool to find the infinite sequence.