
CBSE Important Questions›

CBSE Previous Year Question Papers›
 CBSE Previous Year Question Papers
 CBSE Previous Year Question Papers Class 12
 CBSE Previous Year Question Papers Class 10

CBSE Revision Notes›

CBSE Syllabus›

CBSE Extra Questions›

CBSE Sample Papers›
 CBSE Sample Papers
 CBSE Sample Question Papers For Class 5
 CBSE Sample Question Papers For Class 4
 CBSE Sample Question Papers For Class 3
 CBSE Sample Question Papers For Class 2
 CBSE Sample Question Papers For Class 1
 CBSE Sample Question Papers For Class 12
 CBSE Sample Question Papers For Class 11
 CBSE Sample Question Papers For Class 10
 CBSE Sample Question Papers For Class 9
 CBSE Sample Question Papers For Class 8
 CBSE Sample Question Papers For Class 7
 CBSE Sample Question Papers For Class 6

ISC & ICSE Syllabus›

ICSE Question Paper›
 ICSE Question Paper
 ISC Class 12 Question Paper
 ICSE Class 10 Question Paper

ICSE Sample Question Papers›
 ICSE Sample Question Papers
 ISC Sample Question Papers For Class 12
 ISC Sample Question Papers For Class 11
 ICSE Sample Question Papers For Class 10
 ICSE Sample Question Papers For Class 9
 ICSE Sample Question Papers For Class 8
 ICSE Sample Question Papers For Class 7
 ICSE Sample Question Papers For Class 6

ICSE Revision Notes›
 ICSE Revision Notes
 ICSE Class 9 Revision Notes
 ICSE Class 10 Revision Notes

ICSE Important Questions›

Maharashtra board›

RajasthanBoard›
 RajasthanBoard

Andhrapradesh Board›
 Andhrapradesh Board
 AP Board Sample Question Paper
 AP Board syllabus
 AP Board Previous Year Question Paper

Telangana Board›

Tamilnadu Board›

NCERT Solutions Class 12›
 NCERT Solutions Class 12
 NCERT Solutions Class 12 Economics
 NCERT Solutions Class 12 English
 NCERT Solutions Class 12 Hindi
 NCERT Solutions Class 12 Maths
 NCERT Solutions Class 12 Physics
 NCERT Solutions Class 12 Accountancy
 NCERT Solutions Class 12 Biology
 NCERT Solutions Class 12 Chemistry
 NCERT Solutions Class 12 Commerce

NCERT Solutions Class 10›

NCERT Solutions Class 11›
 NCERT Solutions Class 11
 NCERT Solutions Class 11 Statistics
 NCERT Solutions Class 11 Accountancy
 NCERT Solutions Class 11 Biology
 NCERT Solutions Class 11 Chemistry
 NCERT Solutions Class 11 Commerce
 NCERT Solutions Class 11 English
 NCERT Solutions Class 11 Hindi
 NCERT Solutions Class 11 Maths
 NCERT Solutions Class 11 Physics

NCERT Solutions Class 9›

NCERT Solutions Class 8›

NCERT Solutions Class 7›

NCERT Solutions Class 6›

NCERT Solutions Class 5›
 NCERT Solutions Class 5
 NCERT Solutions Class 5 EVS
 NCERT Solutions Class 5 English
 NCERT Solutions Class 5 Maths

NCERT Solutions Class 4›

NCERT Solutions Class 3›

NCERT Solutions Class 2›
 NCERT Solutions Class 2
 NCERT Solutions Class 2 Hindi
 NCERT Solutions Class 2 Maths
 NCERT Solutions Class 2 English

NCERT Solutions Class 1›
 NCERT Solutions Class 1
 NCERT Solutions Class 1 English
 NCERT Solutions Class 1 Hindi
 NCERT Solutions Class 1 Maths

JEE Main Question Papers›

JEE Main Syllabus›
 JEE Main Syllabus
 JEE Main Chemistry Syllabus
 JEE Main Maths Syllabus
 JEE Main Physics Syllabus

JEE Main Questions›
 JEE Main Questions
 JEE Main Maths Questions
 JEE Main Physics Questions
 JEE Main Chemistry Questions

JEE Main Mock Test›
 JEE Main Mock Test

JEE Main Revision Notes›
 JEE Main Revision Notes

JEE Main Sample Papers›
 JEE Main Sample Papers

JEE Advanced Question Papers›

JEE Advanced Syllabus›
 JEE Advanced Syllabus

JEE Advanced Mock Test›
 JEE Advanced Mock Test

JEE Advanced Questions›
 JEE Advanced Questions
 JEE Advanced Chemistry Questions
 JEE Advanced Maths Questions
 JEE Advanced Physics Questions

JEE Advanced Sample Papers›
 JEE Advanced Sample Papers

NEET Eligibility Criteria›
 NEET Eligibility Criteria

NEET Question Papers›

NEET Sample Papers›
 NEET Sample Papers

NEET Syllabus›

NEET Mock Test›
 NEET Mock Test

NCERT Books Class 9›
 NCERT Books Class 9

NCERT Books Class 8›
 NCERT Books Class 8

NCERT Books Class 7›
 NCERT Books Class 7

NCERT Books Class 6›
 NCERT Books Class 6

NCERT Books Class 5›
 NCERT Books Class 5

NCERT Books Class 4›
 NCERT Books Class 4

NCERT Books Class 3›
 NCERT Books Class 3

NCERT Books Class 2›
 NCERT Books Class 2

NCERT Books Class 1›
 NCERT Books Class 1

NCERT Books Class 12›
 NCERT Books Class 12

NCERT Books Class 11›
 NCERT Books Class 11

NCERT Books Class 10›
 NCERT Books Class 10

Chemistry Full Forms›
 Chemistry Full Forms

Biology Full Forms›
 Biology Full Forms

Physics Full Forms›
 Physics Full Forms

Educational Full Form›
 Educational Full Form

Examination Full Forms›
 Examination Full Forms

Algebra Formulas›
 Algebra Formulas

Chemistry Formulas›
 Chemistry Formulas

Geometry Formulas›
 Geometry Formulas

Math Formulas›
 Math Formulas

Physics Formulas›
 Physics Formulas

Trigonometry Formulas›
 Trigonometry Formulas

CUET Admit Card›
 CUET Admit Card

CUET Application Form›
 CUET Application Form

CUET Counselling›
 CUET Counselling

CUET Cutoff›
 CUET Cutoff

CUET Previous Year Question Papers›
 CUET Previous Year Question Papers

CUET Results›
 CUET Results

CUET Sample Papers›
 CUET Sample Papers

CUET Syllabus›
 CUET Syllabus

CUET Eligibility Criteria›
 CUET Eligibility Criteria

CUET Exam Centers›
 CUET Exam Centers

CUET Exam Dates›
 CUET Exam Dates

CUET Exam Pattern›
 CUET Exam Pattern
Infinite Geometric Series Formula
The sum of an infinite geometric sequence yields an Infinite Geometric Series Formula. In this series, there would be no final term. The infinite geometric series has the formula as a1+a1r+a1r2+a1r3+…, where a1 is the first term and r is the common ratio.
Quick Links
ToggleWhen the common ratio in an infinite geometric series is greater than one, the terms in the Infinite Geometric Series Formula grow larger and larger and adding the larger integers yields no final answer. Infinity is the only feasible answer. As a result, one does not consider the common ratio bigger than one for an infinite geometric series.
What Is Infinite Geometric Series Formula?
The Infinite Geometric Series Formula is similar to the arithmetic sequence, except that each term is multiplied by an additional factor of r. The r’s exponent will be one less than the term number. The first term has never been multiplied by r. (exponent on r is 0). The second term has already been multiplied by r. The third word has twice been multiplied by r, and so on.
Another type of geometric series is the Infinite Geometric Series Formula. The sum of an infinite geometric sequence yields an infinite geometric series.
When the ratio is greater than one, the terms in the Infinite Geometric Series Formula grow larger and larger, and if one adds larger and larger integers indefinitely, they will receive infinity as an answer. When the magnitude of the ratio is bigger than one, one does not deal with infinite geometric series.
The magnitude of the ratio cannot be one because the series would no longer be geometric and the sum formula would have a division by zero.
A geometric series can be stated as the sum of the first term and a multiple of the common ratio since each term is a common multiple of the term that came before it. If a1 is the first term, an is the nth term, and r is any geometric sequence’s common ratio, then an = a1 rn1.
A geometric series is simply a geometric sequence that has been multiplied by itself. akin to this
1 + 2 + 4 + 8 + 16 + 32 + …
It is written as the sum of all the terms rather than simply listing them with commas between them.
The same sigma notation is applied here as well like in the arithmetic series. The numbers in this series will begin at n = 1 and continue all the way to infinity. In this way, the geometric series is special.
The sequence terms will grow quite huge if the common ratio r is more than one. Adding excessively huge numbers makes it nearly hard to obtain the outcome. The solution in this situation can be regarded as endless. It is possible to determine the common ratio’s total when its value ranges between 1 and 1. Therefore, it can be claimed that r<1 is a legitimate value for the sum of an infinite geometric series. S can be used to symbolise the sum. As the sequence of the sum converges closer to a specific value, an infinite geometric series with a fixed sum is referred to as a convergent series. If r > 1, the series is divergent, and since the numbers keep becoming bigger and bigger in a sequential manner, the sum will eventually be infinite (and thus there will be no definitive sum). Students can use the sequence “10 + 20 + 40 + 80 +…” as an illustration. The common ratio in this situation would be 2. As they can see, the values keep increasing as the series goes on indefinitely, making it impossible for them to reach a certain sum.
Examples using Geometric Infinite Series Formula
Students are advised to keep revising the theories of topics. All the questions can be solved well after complete revision. Students are advised to practice examples related to the Infinite Geometric Series Formula. If students are stuck while solving questions related to the Infinite Geometric Series Formula they can make use of the solutions available on Extramarks. The NCERT solutions provided by Extramarks are beneficial for solving questions regarding the Infinite Geometric Series Formula.
FAQs (Frequently Asked Questions)
1. What is the Infinite Geometric Series Formula?
The Infinite Geometric Series Formula is represented as a1+a1r+a1r2+a1r3+…, where a1 is the first term and r is the common ratio. The Infinite Geometric Series Formula is a very important concept.
2. Which is the best place to access NCERT Solutions for Mathematics?
The Extramarks website and mobile application have authentic NCERT solutions that students can use to solve exercises in each chapter. Extramarks has multiple practice materials that students can make use of to score well in their upcoming examinations.