Sum of Infinite Geometric Progression Calculator

✖The First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+10% -10%
✖The Common Ratio of Infinite Progression is the ratio of any term to its preceding term of an Infinite Progression.ⓘ Common Ratio of Infinite Progression [r_∞]			+10% -10%

✖The Sum of Infinite Progression is the summation of the terms starting from the first term to the infinite term of given infinite Progression.ⓘ Sum of Infinite Geometric Progression [S_∞]

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Sum of Infinite Geometric Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sum of Infinite Progression = First Term of Progression/(1-Common Ratio of Infinite Progression)
S_∞ = a/(1-r_∞)
This formula uses 3 Variables

Variables Used

Sum of Infinite Progression - The Sum of Infinite Progression is the summation of the terms starting from the first term to the infinite term of given infinite Progression.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
Common Ratio of Infinite Progression - The Common Ratio of Infinite Progression is the ratio of any term to its preceding term of an Infinite Progression.

STEP 1: Convert Input(s) to Base Unit

First Term of Progression: 3 --> No Conversion Required
Common Ratio of Infinite Progression: 0.8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_∞ = a/(1-r_∞) --> 3/(1-0.8)

Evaluating ... ...

S_∞ = 15

STEP 3: Convert Result to Output's Unit

15 --> No Conversion Required

FINAL ANSWER

15 <-- Sum of Infinite Progression

(Calculation completed in 00.020 seconds)

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Created by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has created this Calculator and 200+ more calculators!

Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

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< Infinite Geometric Progression Calculators

Sum except First N Terms of Infinite Geometric Progression

LaTeX Go Sum except First N Terms of Infinite Progression = (First Term of Progression*Common Ratio of Infinite Progression^Index N of Progression)/(1-Common Ratio of Infinite Progression)

Sum of Infinite Geometric Progression

LaTeX Go Sum of Infinite Progression = First Term of Progression/(1-Common Ratio of Infinite Progression)

< Geometric Progression Calculators

Sum of First N Terms of Geometric Progression

LaTeX Go Sum of First N Terms of Progression = (First Term of Progression*(Common Ratio of Progression^Index N of Progression-1))/(Common Ratio of Progression-1)

Nth Term of Geometric Progression

LaTeX Go Nth Term of Progression = First Term of Progression*(Common Ratio of Progression^(Index N of Progression-1))

Sum of Infinite Geometric Progression

LaTeX Go Sum of Infinite Progression = First Term of Progression/(1-Common Ratio of Infinite Progression)

Common Ratio of Geometric Progression

LaTeX Go Common Ratio of Progression = Nth Term of Progression/(N-1)th Term of Progression

Sum of Infinite Geometric Progression Formula

LaTeX Go

Sum of Infinite Progression = First Term of Progression/(1-Common Ratio of Infinite Progression)
S_∞ = a/(1-r_∞)

What is a Geometric Progression?

In Mathematics a Geometric Progression or simply GP also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed real number called the common ratio. For example, the sequence 2, 6, 18, 54,... is a Geometric Progression with common ratio 3. If the sum of all terms in the progression is a finite number or if the infinite sum of the progression exists then the we say it is an Infinite Geometric Progression or Infinite GP. And if the infinite sum of the progression does not exist, then it is a Finite Geometric Progression or Finite GP. If the absolute value of the common ratio is greater than 1 then the GP will be a Finite GP and if it is less than 1 then the GP will be an Infinite GP.

How to Calculate Sum of Infinite Geometric Progression?

Sum of Infinite Geometric Progression calculator uses Sum of Infinite Progression = First Term of Progression/(1-Common Ratio of Infinite Progression) to calculate the Sum of Infinite Progression, The Sum of Infinite Geometric Progression formula is defined as the summation of the terms starting from the first term to the infinite term of given Infinite Geometric progression. Sum of Infinite Progression is denoted by S_∞ symbol.

How to calculate Sum of Infinite Geometric Progression using this online calculator? To use this online calculator for Sum of Infinite Geometric Progression, enter First Term of Progression (a) & Common Ratio of Infinite Progression (r_∞) and hit the calculate button. Here is how the Sum of Infinite Geometric Progression calculation can be explained with given input values -> 15 = 3/(1-0.8).

FAQ

What is Sum of Infinite Geometric Progression?

The Sum of Infinite Geometric Progression formula is defined as the summation of the terms starting from the first term to the infinite term of given Infinite Geometric progression and is represented as S_∞ = a/(1-r_∞) or Sum of Infinite Progression = First Term of Progression/(1-Common Ratio of Infinite Progression). The First Term of Progression is the term at which the given Progression starts & The Common Ratio of Infinite Progression is the ratio of any term to its preceding term of an Infinite Progression.

How to calculate Sum of Infinite Geometric Progression?

The Sum of Infinite Geometric Progression formula is defined as the summation of the terms starting from the first term to the infinite term of given Infinite Geometric progression is calculated using Sum of Infinite Progression = First Term of Progression/(1-Common Ratio of Infinite Progression). To calculate Sum of Infinite Geometric Progression, you need First Term of Progression (a) & Common Ratio of Infinite Progression (r_∞). With our tool, you need to enter the respective value for First Term of Progression & Common Ratio of Infinite Progression and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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