A Result

These results are interesting. 

Books needed

Justification -

I wrote the area of a perfect and hence simple right angled triangle is zero. And I also wrote that I need this statement for proofs. Well what I was talking of was about analysis. Hence a book on analysis.

I wrote n should be treated as pi and 2n as pi squared. What I was talking of was about infinity. Hence a book on infinity by the great man himself. Euler.

The three consecutive numbers and four consecutive number theory has given me hope in a subject I dreaded. Algebra. I want to see how much does this concept relevant. Hence books on Algebra by great men themselves. Euler. Maclaurin.

Notebooks of Ramanujan, Disquisitiones Arithmeticae and a book on Niels Henrik Abel are mathematical biographies that I wish to possess.

Is it valid?

Made it !!

At last !!

I wanted to put four variables and make an equation like Niels Henrik Abel.

I have made it. Here it is. It is exact. ( I have checked only for 2 values, though.)

I shall check on this more. And blog if there is an error. 

Have a nice day, dear blog readers !!

An exact expression

I was trying hard to get an exact equation. There were many approximate results with my four consecutive numbers and three consecutive numbers theory.
I made this one. This is an exact equation. Put any values for n and a. And bingo !! You can verify that the results hold exactly.(Still if there is any discrepancy, do let me know)

Check out these two expressions

The two expressions are approximately equal. Not exactly equal. But approximately. Till 7 places of decimals or more. Also the number of terms in LHS and RHS in both are odd number of terms. Not even number. In case the number of terms are even number then it gives some other value.
Again, many readers of my blog may be confused. I am sorry for that. Perhaps I need to write a paper on this. I shall think about it.

In total I made three approximate expressions. I am putting all the three expressions here for the help of the reader.

Have a nice day, my dear readers.

At present . . .

I watched the movie Khoj(2017) recently. I liked it immensely. It is a Bengali/Hindi movie. It is a detective story. The locales were superb. The music was excellent. And if you start watching the movie, then you cannot help but watch till the end. This movie was recommended by Youtube logic. It has English subtitles.
I am not in a position to hear radio as my travel time is highly reduced. As compared to my Delhi life earlier. Therefore the pleasure of hearing new songs and using the Shazam app for the song name is no longer there. I feel terribly sad. This is a big sacrifice I had to make as I am a big songs lover. Internet and the search logic is hardly an answer to this. Because the pleasure of listening to a fantastic new song is only there in FM radio. This is how I feel. I really miss those listening to "Suno na sangemarmar" or "Khamoshiyan" in FM radio in Delhi roads. Dukh hondha hai, pape !!(Punjabi)
It is great that India has come up with COVAXIN, a vaccine for coronavirus. It is a great feat by our scientists and medical doctors. The doctors and the medicos have been working so hard for the last few months. I am sure this vaccine will work and give freedom from this disease.
My good wishes to all of my blog readers !!