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Raghavendra'sAnalysis

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Raghavendra's Analysis

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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 + . . . + n3  etc. 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.

 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.

How To Confirm that Current education system teaches only tricks but not MATHEMATICS?

Original product means more features and more advantages. Do you like to spend your more money to buy a duplicate product which has one day warranty and costs more than the original?

Like that there is a huge difference between answer getting tricks and algebraic math (True Math = Raghavendra's analysis). Unfortunately this truth never told to students for some reasons.!?

Examples to check the derivation in current education curriculum is MATH or TRICK?

Sum Of Geometric Progression Formula Derivation

Consider the derivation of the formula to find the sum of Geometric Series.

Currently students are learning the following method:

Let Sn be the Sum of first n terms.

Sn = a + ar + ar2 + ar3 + . . . + arn-1    ----(1)

Now Multiply r to both sides, (1) becomes

rSn = ar + ar2 + ar3 + ar4 + . . . + arn   ----(2)

Subtracting (2) from (1) we get:

Sn - rSn =  a - arn

Sn( 1- r) = a (1 - r)n

Therefore,           Sn = a (1 - r)n / (1 - r)   (r≠1)

Is the above derivation is Math? that the whole world is learning!

Did you observed the Steps in the derivation? Any following below questions came in youe mind? Think about the questions below which creates you the awareness on quality mathematics education!

Why To assume answer as Sn even before the start of any calculations?

Why to take the term extra data Sn insted of getting formula with only calculations on given terms like a, ar, etc.?

Why to Multiply 'r' to both sides of (1) ? If one forgot this step can he able to derive formula? Or one must need to By heart this step?

Why to subtract (2) from (1)? Is it possible to get formula if this step was forgotten?

After Doing all these tricks, the final answer will be in the format of Sn = a (1 - r)n / (1 - r)  but not like:

a + ar + ar2 + ar3 + . . . + arn-1  = a (1 - r)n / (1 - r)

After learning all these tricks, Is it possible to use same tricks to derive formula for other series? (Answer is No)

Hence, learning the above method help the students to only get marks but not the knowledge of deriving formulas! And knowledge is in true math.

Solution: The one and only solution to come out from solving problems from By hearting steps is the learning of raghavendra's analysis; where the beginning of the end of blind and terror mathematics started. Get solution for same problem in one simple step in Raghavendra's analysis.

Devil Tricks Used To Derive formula to find sum of cubes in current education system

Derivation of the formula to find sum of cubes of first n natural numbers:

Step 1: First need to find out what is (k + 1)4 - k4 or need to by heart the identity: (k + 1)4 - k= 4k3 +6k2 + 4k + 1

Step 2: Put K = 1, 2, 3, ..., n So that we get:

24 - 14 = 4(1)3 + 6 (1)2 + 4(1) + 1

34 - 24 = 4(2)3 + 6 (2)2 + 4(2) + 1

44 - 34 = 4(3)3 + 6 (3)2 + 4(3) + 1

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(n – 1)4– (n – 2)4= 4(n – 2)3+ 6(n – 2)2+ 4(n – 2) + 1

n4– (n – 1)4= 4(n – 1)3+ 6(n – 1)2+ 4(n – 1) + 1

(n + 1)4n= 4n3+ 6n2+ 4n + 1

(n + 1)4– 14= 4(13+ 23+ 33+...+ n3) + 6(12+ 22+ 32+ ...+ n2) + 4(1 + 2 + 3 +...+ n) + n

4(13+ 23+ 33+...+ n3) = n4 + 4n3 + 6n2 + 4n - 6(12+ 22+ 32+ ...+ n2) - 4(1 + 2 + 3 +...+ n) - n

Substitute the formula for sum of first n natural numbers and sum of squares of first n natural numbers in the above we get:

4(13+ 23+ 33+...+ n3) = n4 + 4n3 + 6n2 + 4n - 6[n(n+1)(2n+1)/6] - 4[n(n+1)/2] - n

4(13+ 23+ 33+...+ n3) = n4 + 4n3 + 6n2 + 4n - n(2n2+3n+1) - 2n (n+1) - n

4(13+ 23+ 33+...+ n3) = n4 + 2n3 + n2 = n2 ( n+ 1)2

Hence, (13+ 23+ 33+...+ n3) = [n ( n+ 1)]2 /4

Let's ask some commonsense questions about the derivation o create awareness quality math education!

Just observe the derivation and its steps.

1.  It's the problem to find the formula to find sum of some numbers!, commonsence question come here that, why can't we can get the formula just by doing calculations like addition, subtraction, etc. on the given numbers?

2.  Why we need to take identity "(k + 1)4 - k= 4k3 +6k2 + 4k + 1" ? which is not related to both the question and the answer!

3.  Why it is not possible to derive the formula just by doing calculations on some few terms? Say 13+ 23+ 33 + 43 ?

4.  The derivation is difficult to teach even for the experts! What knowledge, opinion and interest these tricks creates on students mind which includes By hearting identity, complicated and big calculations and different formulas?

5.  A teacher or a tutor can help the student to only understand the tricks used in the derivations! Can he show the way to student to escape from these trouble steps?

6.  Can student remember this even after this exam? and Why? Students are learning these types of methods only for the aim of getting marks! They soon forgot the methods as it won't help him in understanding the subjects or other problems!

Solution: The one and only solutions to save students from the blind mathematics is Raghavendra's analysis. If the current education system solutions like tigers; for same problems the solutions look like ants; because Raghavendra's analysis gives automatic algebraic solutions which includes only very simple calculations.

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 Question? 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

 Preface     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.