Infinite Series Calculator

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 

Σ₀ ^∞ rⁿ

where

o is the upper limit.

∞ is the lower limit.

r is the function.

The infinite sequence of a function is 

Σ₀^∞ rⁿ = 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 Σ₀^∞ 1/5ⁿ?

Solution:

Given, Σ₀^∞ 1/5ⁿ

r = 1/5

Apply the formula,

Σ₀^∞ rⁿ = 1/(1-r)

Σ₀^∞ (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.

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 Σ₀^∞ rⁿ = `1/(1-r)`.

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

A standard form of the infinite sequence is Σ₀ ^∞ rⁿ.

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

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