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Real Derivations For Series (New) 


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Easy formulas for Binary Octal Arithmetic operations(As Easy as Decimal Arithmetic)



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Most Surprising Division

Now rapidly Divide any number by 9,99, 999, etc. just doing only addition calculations.

Experience the joy of doing division without doing any divisions from Number System book. The book also contains amazing derivations to automatically get formulas.


Sum Of Natural Numbers

   Raghavendra's analysis is the one and only TRUE algebraic method to derive formulas for finding sums of:

a + ar + ar2 + ar3 + ...+ arn-1 (GP)

1 + 2 + 3 + . . . + n

12 + 22 + 32 + . . . + n2  

13 + 23 + 33 + . . . + netc.

So what method you want Learn?


Can You Imagine This?

    Can you imagine to do the following calculations rapidly just learning one method?

   Derive formulas to find sums Geometric progression, sums of natural numbers, first n squares, cubes, sum of odd numbers, breaking one series into sums of other series, converting one series to another, deriving formulas for finding sums of different types of series, derive 5 more new methods for rapid converting decimal number to binary, octal, hexadecimal etc. and vice versa., developing new and easy methods for binary, octal, etc. arithmetic operations, develop new number system, arithmetic operations, developing methods to convert decimal number to binary, binary arithmetic operations in normal calculator, etc.

   Difficult to believe that different problems of different chapters possible to be solved in one method? 'Raghavendra's Analysis' the new invention made possible all these very easily using only kids level mathematics calculations like addition, subtraction, multiplication and division of some small numbers.

Easy Intelligent Math Or Difficult poor Math? Only Two choices! Change To New Or Follow the Failed Ways. 


Raghavendra's Analysis

   List of Series Sums formulas Derived Using Raghavend's Analysis.Click Here.

   List of new and fastest number system conversion methods invented (derived) using Raghavendra's analysis. Click Here.

   Name of New Number System and Arithmetic operations invented using Raghavendra's analysis.

1. Decimal Coded Binary Number System

2. Hetero Base Arithmetic Operations


Our Challenge

   Presently students are learning answers getting neat tricks as mathematics. Because their teachers teaches that lessons without telling the them the truth.

   Learning Raghavendra's analysis is must needed to study or teach derivations for formulas to find sums of Geometric progression,  sums of first n natural numbers, squares, cubes, etc.

   So for those who wants to learn or teach true math, there is only one choice; that is Raghavendra's Analysis. Its Time for students to demand or learn Real and Quality math education. Aware Now


How to write a program to convert any decimal number (+ve or -ve) to binary, octal and vice versa using only one formula?

   Using 'Quotient method' a new formula invented using Raghavendra's analysis gives the algorithm to write the said program easily. The research book also contains extremely powerful formulas to easily develop several verities of useful software.  





Number System: Auotomatic Algebraic Solutions is an innovative text that introduces high quality methods for easily learning various concepts of number system. It is the outcome of deep analysis on the number system. The book is very useful for students, scientists, engineers, etc.

Chapter 1 covers many high speed methods for division by 9, 99, 999, etc, formula to create fast methods for any division. The division methods are also useful for computer programs.

Chapter 2 covers Raghavendra’s analysis (R-analysis) and its applications. R-analysis is the unique key for solving several problems. It is the easiest and best way for algebraically solving various problems of the number system.

There is only one method is there to algebraically derive formulae for finding the sums of first ‘n’ natural numbers, squares, cubes, etc. That method is R-analysis. Other than R-analysis there are several ways to derive formulae for finding the sums of these series, but none is merely an automatic algebraic derivation where we can just turn the crank and get the answer with out any insight.

For example in one previously used method, it is used a neat trick to derive formula for finding the sum of first ‘n’ natural numbers  [that trick is: Sn = 1 + 2 + 3 + … + n and Sn = n + … + 3 + 2 + 1   2Sn =  (n + 1) + (n + 1) + … up to n times (n + 1)       2Sn = n (n + 1)  Sn = n (n + 1) / 2]  but the same method (trick) completely fails to derive formula for finding the sum of other series;

similarly, in another method, {which is completely depend on the result of the   [(n + 1)2 – n]} based on the result of [(n + 1)2 – n], remaining steps are created to derive formula. But same derivation cannot be possible if we give any value for ‘n’ in the starting steps, i.e., in the first step if we give any value for n, say for example 4, then we cannot able to do the same derivation from the result of [(4 + 1)2 – 4].


The number system conversion methods developed using R-analysis is very useful for rapidly converting any base number to decimal equivalent and vice versa, useful for binary, octal etc. arithmetic operations and hetero base arithmetic operations, useful to invent many useful concepts of the number system and we study the applications of these conversion methods in the Chapter 3.

Chapter 3 covers Decimal Coded Binary (DCB) number system and detailed study of Quotient, Quotient Difference, Difference, Add and Step methods (which are created using R-analysis).

Using the Quotient method we can convert base x (when x ≥ 8) number to decimal number more rapidly than any other usual methods and using the same method we can perform decimal number to binary, octal, etc. conversion, Multi base conversions, binary, octal, etc. arithmetic operations, etc.

The Quotient method is very good for computer program, since in one program (formula) we can rapidly convert base x number to decimal equivalent and vice versa; it convert negative numbers also. But if we use usual method in the programs, it fails to convert negative numbers and it requires more calculations.

The Difference method is useful for rapidly converting any base number to decimal equivalent and Quotient Difference method is useful for rapidly converting base x (x ≥ 8) number to decimal equivalent.

Using the Add method, we can add up to nine binary numbers at a time and using same method we can very easily perform binary multiplication, Hetero base addition/multiplication, converting sum or products of binary numbers to DCB number, converting DCB number to binary equivalent, etc.

  The DCB number system and Hetero base arithmetic operations are new to mathematics. A formula is developed for converting decimal number to DCB by studying the Add method. Converting decimal number to DCB number is very useful for rapidly converting decimal number to binary equivalent; since, we can rapidly convert any DCB number to binary equivalent very easily.

Using the Add method, we can easily perform decimal number to binary conversion, binary and Hetero base arithmetic operations in a non-calculator (for example calculators in the mobile phone). But we cannot do this in normal calculator without learning the Add method; even in widely used scientific calculators we can perform only some limited calculations, for example we cannot do binary arithmetic operations for the numbers with fractions, and for binary division it gives only integer part of the answer, etc. 

Using the Step method, we can convert decimal number to binary, octal etc. It is also useful for converting all terms of sequence to binary, octal etc. equivalent and to find out various new concepts of the number system. We can also perform Step method calculations in calculator.

The R-analysis, new formulae, conversion methods, rapid calculations methods, various new concepts in this text are very much useful for solving various mathematical problems easily, extremely useful for several research and technological applications.

I would like to thank Sri Satish Vaman Naik Sir, for his encouragement, giving expert guidelines to improve the text and for writing foreword to this book. I would also like say thank for all who contributed to the success of this book in one way or another.  

I welcome any comments concerning the text. Comments may be forwarded to the following email address: or

                                                                Raghavendra Lingayya















































Raghavendra,s Analysis: Better than Imaginations



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Which is the one and only Genuine method to derive formulas for finding sums of Geometric progression, first n natural numbers, squares, cubes, etc.?


What a surprise? If many numbers are added to one number, the total not changes! How?

Learn DCB(New) number system!


Is it Possible to do binary arithmetic operations including fractions in a normal calculator?

   Yes, using "Add method" even children can do these just like playing games.

   Note 1 : It is not possible to do fractional parts calculation of binary arithmetic operations top scientific calculator; but "Add Method" makes this possible even in normal calculator.

  Note 2 : "Add Method" is the new method introduced to math  from "Number System" text. 


Headache, Tension from Math Virus?

   Get Freedom from lots of terror solutions, complex formulas and calculations just by learning one method Raghavendra's Analysis.


Kids Vs College Students

   Kids easily learned and solved Higher education level complex problems faster than University students. "Raghavendra's analysis" is the secret behind this shocking news. 


Kick Terror Math Before It Harms

   Learning or By hearting the poor and  terror answer getting solutions makes heavy damages in the students mind resulting them to accept foundationless thoughts without thinking. Only Raghavendra's Analysis opens students eyes to explore the useful truth and secrets of the number system. 



   This book consists of ample of invaluable information's which help the students to a great extent. This book aims primarily to creat intrest in students. Read More



    Number System: Automatic Algebraic Solutions is an innovative text that introduces high quality methods for easily learning various concepts of numner system.

Number System: Automatic Algebraic Solutions: is the must book for true and high quality education. No other book can provide better and fast solutions than this. 

Are You Ready For The Next Generation Mathematics?

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