Sum infinite GP when r is less than one Calculator

Category	Math ↺
Math	Sequence and Series ↺
Sequence-And-Series	Geometric Progression ↺

✖First term is the initial term of a series or any sequence like arithmetic progression, geometric progression etc. It is generally denoted with 'a'. ⓘ First term [a]			+10% -10%
✖Common Ratio is the constant factor between consecutive terms of a geometric sequence.ⓘ Common Ratio [r]			+10% -10%

✖Sum of First n terms denoted the sum of first n terms occuring in a progression like Arithematic Progression, Geometric Progression, Harmonic Progression.ⓘ Sum infinite GP when r is less than one [S_n]

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Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has created this Calculator and 100+ more calculators!

Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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

< 11 Other formulas that you can solve using the same Inputs

Sum of first n terms in an AP when common difference is given

Sum of First n terms=(total terms/2)*(2*First term+(total terms-1)*Common difference) GO

Position of pth term when pth term, first term & common difference is given

Position in series p=((pth Term-First term)/Common difference)+1 GO

Common Difference when first term & pth term are given

Common difference=(pth Term-First term)/(Position in series p-1) GO

Number of terms when Sum of first n terms, first term & last term are given

total terms=((2*Sum of First n terms)/(First term+Last term)) GO

Sum of first n terms in an AP when last term is given

Sum of First n terms=(total terms/2)*(First term+Last term) GO

Common Difference when first term, last term & number of terms are given

Common difference=((Last term-First term)/(total terms-1)) GO

Last term when number of terms, first term & common difference are given

Last term=((total terms-1)*Common difference)+First term GO

Number of terms of in an Arithematic Progression

total terms=((Last term-First term)/Common difference)+1 GO

Nth term of an Arithematic Progression

Nth term=First term+(total terms-1)*Common difference GO

Nth term of AP

Nth term=First term+(term number-1)*Common difference GO

Nth term of GP

Nth term=First term*(Common Ratio^(value of n-1)) GO

< 10 Other formulas that calculate the same Output

Sum of first n terms of AGP

Sum of First n terms=((First term-(First term+(total terms-1)*Common difference)*(Common Ratio^total terms))/(1-Common Ratio))+(Common difference*Common Ratio*(1-Common Ratio^(total terms-1))/(1-Common Ratio)^2) GO

Sum of first n terms in an AP when common difference is given

Sum of First n terms=(total terms/2)*(2*First term+(total terms-1)*Common difference) GO

Sum of first n terms where r>1

Sum of First n terms=First term*(((Common Ratio^total terms)-1)/(Common Ratio-1)) GO

Sum of first n terms in a finite GP

Sum of First n terms=(First term*((Common Ratio^value of n)-1))/(Common Ratio-1) GO

Sum of squares of first n natural numbers

Sum of First n terms=(value of n*(value of n+1)*(2*value of n+1))/6 GO

Sum of first n terms in an AP when last term is given

Sum of First n terms=(total terms/2)*(First term+Last term) GO

Sum of cubes of first n natural numbers

Sum of First n terms=((value of n*(value of n+1))^2)/4 GO

Sum of first n natural numbers

Sum of First n terms=(value of n*(value of n+1))/2 GO

Sum of first n even natural numbers

Sum of First n terms=(value of n*(value of n+1)) GO

Sum of first n odd natural numbers

Sum of First n terms=(value of n)^2 GO

Sum infinite GP when r is less than one Formula

Sum of First n terms=First term/(1-Common Ratio)
S<sub>n</sub>=a/(1-r)

More formulas

Nth term of GP GO

Sum of first n terms in a finite GP GO

nth term from end in a finite GP GO

nth term from the end of finite GP when last term and common ratio is given GO

Common Ratio GO

Geometric Mean of two numbers GO

Sum of infinite GP except first n terms when r<1 GO

Geometric Mean when Harmonic Mean and Arithmetic Mean is given GO

What is infinite GP?

An infinite GP is a GP with infinite number of terms.When the ratio has a magnitude greater than 1, the terms in the sequence will get larger and larger, and the if you add larger and larger numbers forever, you will get infinity for an answer.So, when common ratio r is less than 1, then only the above formula is applicable.

How to Calculate Sum infinite GP when r is less than one?

Sum infinite GP when r is less than one calculator uses Sum of First n terms=First term/(1-Common Ratio) to calculate the Sum of First n terms, Sum infinite GP when r is less than one is the sum of all the terms in a geometric progression which contains infinite terms. . Sum of First n terms and is denoted by S_n symbol.

How to calculate Sum infinite GP when r is less than one using this online calculator? To use this online calculator for Sum infinite GP when r is less than one, enter First term (a) and Common Ratio (r) and hit the calculate button. Here is how the Sum infinite GP when r is less than one calculation can be explained with given input values -> -1 = 1/(1-2).

FAQ

What is Sum infinite GP when r is less than one?

Sum infinite GP when r is less than one is the sum of all the terms in a geometric progression which contains infinite terms. and is represented as S_n=a/(1-r) or Sum of First n terms=First term/(1-Common Ratio). First term is the initial term of a series or any sequence like arithmetic progression, geometric progression etc. It is generally denoted with 'a'. and Common Ratio is the constant factor between consecutive terms of a geometric sequence.

How to calculate Sum infinite GP when r is less than one?

Sum infinite GP when r is less than one is the sum of all the terms in a geometric progression which contains infinite terms. is calculated using Sum of First n terms=First term/(1-Common Ratio). To calculate Sum infinite GP when r is less than one, you need First term (a) and Common Ratio (r). With our tool, you need to enter the respective value for First term and Common Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Sum of First n terms?

In this formula, Sum of First n terms uses First term and Common Ratio. We can use 10 other way(s) to calculate the same, which is/are as follows -

Sum of First n terms=(total terms/2)*(2*First term+(total terms-1)*Common difference)
Sum of First n terms=(total terms/2)*(First term+Last term)
Sum of First n terms=(First term*((Common Ratio^value of n)-1))/(Common Ratio-1)
Sum of First n terms=(value of n*(value of n+1))/2
Sum of First n terms=(value of n*(value of n+1)*(2*value of n+1))/6
Sum of First n terms=((value of n*(value of n+1))^2)/4
Sum of First n terms=First term*(((Common Ratio^total terms)-1)/(Common Ratio-1))
Sum of First n terms=((First term-(First term+(total terms-1)*Common difference)*(Common Ratio^total terms))/(1-Common Ratio))+(Common difference*Common Ratio*(1-Common Ratio^(total terms-1))/(1-Common Ratio)^2)
Sum of First n terms=(value of n*(value of n+1))
Sum of First n terms=(value of n)^2

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