Expression on 2022_09_01

 I present the following expression today.

And here are the calculations done in Wolfram Alpha which confirms the validity of the expression.

Have a nice day !!

Sundar Pichai

 

Sundar Pichai is wonderful.  He has revolutionized the way Google works.  Or the way we work with Google. 

Shopping,  making friends,  expressing yourself,  travel, getting directions etc. etc. has become so easy now. Thanks to his vision as a great team man and a great industry leader.

America especially has been too good and too kind and too generous to me personally . I can never erase the help given by Wolfram, Andrew Loomis,  Lou Darvas, Tom Richmond,  Scott Harris,  Wikipedia founders and now Sundar Pichai. 

I am inspired.  I also try to pass on my knowledge pieces and information the way Americans do. That is my internet philosophy.  

Have a great day !!

Product Sigma equivalence

 I have applied and am publishing the following.

The two screenshot from Wolfram Alpha support my above statement.

Hope you have a fine day !!

Nicomachus formula reapplied

I have reapplied the Nicomachus formula. Nicomachus was an ancient Greek mathematician who is known for the formula of sum of cubes of n numbers. The formula was adopted to my consecutive number theory.

The formula reapplied is

The following are the results from Wolfram Alpha asserting that the formula is correct for n =101.

Hope you have a nice day !!

A childhood dream

When I was a kid, I learnt (a+b) the whole squared and (a+b) the whole cubed formula. I would wonder why there is no formula for a^n+b^n.

Today, I am partially fulfilling this dream of mine with consecutive numbers. For, I have made a somewhat equivalent formula.

The formula is

(Kindly check the formula thoroughly before use. I have checked for two cases and found it okay.)

I am in love with this formula of mine as it mixes up consecutive numbers, factorials and binomials, all three. 

I am sure you will like the above expression.

Have a very nice day !!

A binomial expression today

 I am presenting a binomial expression today.

Hope you like it.

Have a nice day !!

Another new binomial statement

I am hereby presenting another binomial statement. This is a modification of the expression contained in my earlier blog post.

Hope you like it.

Have a nice day !!

A new binomial statement

I have made a new binomial statement. Using the consecutive number theory. 

Hope you like it.

Have a nice day !!

Sixth golden ratio infinite series

Nothing beats the series 0,1,1,2,3,5,8,13, . . . .   or 1+1/(1+1/(1+1/(1+1/ . . . . .  in terms of simplicity and beauty for golden ratio. The first one is due to Fibonacci. The second one is generally known, I think; and there is no specific person.

I try and I develop. With the help of Wolfram Alpha, I have developed the sixth infinite series for golden ratio. It is a little complicated, but the result is obtained.

Here is the screenshot.

Thank you so much Wolfram Alpha.

Have a nice day !!

Root 3

 Root 3 is another difficult expression to get. But using the consecutive number model I have obtained root 3 expression too.

Here are they

Hope you have a nice day !!

Fifth golden ratio infinite series

 I hereby present the fifth golden ratio infinite series expression.

Hope you have a nice day !!

Fourth Golden ratio infinite series

I have made the fourth golden ratio infinite series. The first three golden ratio infinite series are already made into blog post and posted earlier.

This blog post is of the fourth infinite series of golden ratio.

Many may say that these are not of golden ratio. I disagree with them. All the infinite series of golden ratio of mine do exhibit golden ratio properties. They may not be half plus root five by two as such; but certainly are maybe 3/2 plus root5 by two or such equations. 

All the infinite series of mine of golden ratio do exhibit golden ratio properties. They may not have a beauty of 1,1,2,3,5,8,13, . . . . . . .  or 1+1/(1+1/(1+1/(1+1/(1+ . . . . . . ; but they are good only.

Have a nice day !!

Yours delightfully

I got two expressions for root 2. And that is a matter of great delight for me.

First things first. Here are the two expressions for root 2.

Root 2 is important for everyone. Each one of us is standing on two feet balancing in gravity. How does a man stand on his feet? As a child he gained many things from his parents, relatives, friends and neighbors due to "favorable field" of environment. How to stand, speak, body language etc. etc.

Gauss was possibly the greatest mathematician. He was greater than Euler. And he rejected the paper of Niels Henrik Abel stating that it is a work of a crank. I do believe that he was better than Euler in many respects. However, I like Abel so much that I dislike Gauss rejection of Abel's paper. In fact history say that Abel's work in the paper was correct and his work on impossibility of solving quintic equations is a paper of great worth.

Anyways.

Gauss discovery of Gauss constant G is an incomparable genius. The highest point in a distribution mapping. 

G is observed in many phenomenon.

That's all for now folks. Have a great day !!

Basic five binomials with consecutive numbers

I have made basic five binomial statements. Two have been added just now. The older three, I had already made blog posts of.

These basic five can be expanded and used in many ways. Can be made into problems too.

I hope you like them

Have a very nice day !!

A new binomial expression

I am a semi-government servant.  I fulfill Modi Bharati wishes. 

Here is a binomial expression which is great,  I feel. Here we go.

Suprabhatham Bharati Putrajaya.

A New Expression

 A few years back I had submitted the following expression

Today I am submitting another expression based on above

Kindly check the above for correctness before believing the above to be the truth.

Have a very nice day !!

Possible big theory here too

 In my earlier blog post, I showed Wolfram results for 3 consecutive numbers and wrote about a possible big theory.

In this blog post,  I am sharing Wolfram results for 4 consecutive numbers. 

Hope you all have a nice day!!

Possible big theory

Kindly look at the below six expressions. Three of them are similar to the other three. That is a great amount of theory if one could apply brains together.. One person is myself. Who else is interested? Kindly respond in comments.

 Have a nice day !!

What inspires me

I feel proud of Arya Samaj.

I feel proud of Servants of people society. 

These are important thoughts of Delhi people. 

Arya Samajis and Servants of people are called Sanghis(RSS) by many politicians. So poor sighted they are. And these can cause fear and force innocent people to choose Christianity or Islam.

I am afraid that is the reason why I use the words Allah and Jesus in my blog posts.

I am secular and feel okay to use Allah and Jesus in my writings.  Many objections arise in air and I wish to clarify my position. 

Have a nice day !!

Theory of Binomials

 

Binomial Expression 2

A couple of days back I had posted the following expression

And today, I am posting the following binomial expression

hope you have a nice day !!

Abel Binomial Theorems

I remember seeing at least 5 binomial theorems of Niels Abel. But internet works in a funny way. I do not see those pages now. 

I now managed to get two of Abel's many binomial theorems. 

They are

Have a nice day !!

Thank you Wolfram Alpha

I am thankful to Wolfram Alpha more than anything. It was Wolfram Alpha which guided me in my mathematical journey.

The results I am talking of are

Thank you Wolfram Alpha for everything !!

Masala dosa

 

Masala dosa is a thin pancake of rice and urad dal batter saltish and sourish in taste. It is filled with aloo curry in traditional method. Nowadays the fillings have improved and lot many stuffed dosas are available.  

Then I thought of Gauss Newton algorithm

Then I thought of my basic Rational number series not suitable to Mumbai, allahabad and Chennai Mathematical journals.

Have a nice day !!

Some points

 

Not all calculators support 0.5! 

I believe that the first equation can be true. 

For Putnam aspirants

Putnam is American mathematics olympiad sorts. It is conducted every year. MIT guys do well in these exams.  Indians staying in USA are okayish in these exams. 

Putnam has questions in 

Numbers

Geometry

Functions 

Limits

I wish I become a Putnam coach. There is a lot of money. However I have only intuitions.  No steps. With respect to the above four points on Putnam questions my intuitions are

Consecutive number theory 

3 to 4 Consecutive numbers 

Consecutive number binomial function statement

Star Delta convergence test

You teach me problem solving approach.  I give you intuitions.  How about that?

Anyways. 

Take my intuitions.  I don't have much in hand.

May Allah give me something. 

Have a nice day !!

Bhalla Papdi

 

Bhalla papdi is popular in North India. It is thayir vada and flat pani puris in curd, saunth  and spices.

Then I thought of Gauss-Legendre collaboration in pi and other important functions. 

Then I thought of Rational Series and rejection of the ideas contained therein by JRMS and other journals of India.

Vada Pav

 

Vada Pav is a famous dish in western India. It is aloo bonda between pav. It is served with green chutney.

Then I thought of Euler-Maclaurin formula.

Then I thought of JRMS. There was foundation of binomial using rational number series in my paper submitted. I was told paper rejected due to quality.

My good wishes shall always be there.

Particularly, the above expression has been rejected by JRMS for lack of sufficient quality.

I later got the expression published in IJMT.