You may be aware that I have approximate expressions for factorial, to the power n and the next number.
So I tried on Wolfram Alpha using above.
I always thought where there is cos(x) , there is sin(x). And they have same number of parameters.
But not so.
The above happens at only one place. At x = 4 or x=1/4 depending on whether x^n is in numerator or denominator.
Have a nice day!! May God bless us !!
Now that we in India have approximate 2n factorial formula; and now that we in India have approximate (a/b)^n formula; and now that we have the next number approximation; and now that we have many other formulas for approximate functions: . . . . . . it is time that Indian mathematicians apply their brain and work towards approximate integral.
Just as Taylor series gives function as infinite series of to the power n, factorial and next level derivative; I am suggesting a function of approximations with my approximate values of (a/b)^n, (2n)! and next number.
PM Narendra Modi should form a high power mathematics committee to explore, try and make approximate integral statements.
The benefits are Indian people will develop to behave approximately. Indian people will improve intelligence. Indian people will develop devotion.
If you think my idea is even 10 percent feasible, do comment below.
Imagine you never experienced gravity. You were born in space, devoid of much gravitational field. Will you be having bhakti for Shiva? For Vishnu?
Sitting in my home at Ranchi, I am hearing devotional hymns and chants being played on loudspeakers. Chatt festival season, it is. A local festival of Bihar and Jharkhand.
Can there be taal without gravity? Imagine tabla being floating around. Can a tabla player still play the tabla? If he cannot, then there is no rhythm. If there is no rhythm, then there is no hymns. If there are no hymns, how can bhakti be developed?
My earlier approximate formula for 2n!, I believe is devoid of gravitational numbers. So I claim. So I believe.
My point is this. Rhythm may not possible in absence of gravity. Is it possible to see truth, meaning God through my 2n factorial formula?
I wonder.
The (2n)! formula with ((((n+1)(n+2))/2)^n) gave me many sleepless nights since April 2024. On April 2024, I discovered that ((((n+1)(n+2))/2)^n) is approximately connected to (2n)!. But how to give an expression? My education is limited. My mathematical prowess is hardly comparable to champions of IIT JEE.
But I felt it is my duty to complete the formula. Till calculator range. Till 170!. Or when n equals 85.
I carried on. I used the formula of Stirling formula and other expressions of (2n)! to get (2n)! through ((((n+1)(n+2))/2)^n). Well that was incorrect method. But I continued.
Now, I have finally made it. Without the use of any other approximate or accurate formula of (2n)!
Here is the formula
Here is an excel sheet that confirms 99 percent accuracy.
Have a great weekend folks!!
Most of my blog readers might be confused with my earlier blog post.
This post is for them.
Actually 2n factorial formula is much simpler.
They are
And the proof
I managed to get 2n factorial accurately with (((n+1)(n+2))/2)^n.
Here is the operation in Wolfram Alpha.
Here is the value of 100!
For finding 1000!, do like below
And the formula is
Happy Diwali to you all, dear blog readers.
We all have been adding 1+2, then 1+2+3 and then 1+2+3+4 and so on.
This sort of addition can get us 2n!.
It is a simple formula. But never came across this. I thought, let me make a blog post of this.
That's all folks. Wish you all a happy Diwali !!
( I feel I have made an ancient Greek formula. 😁😁😁)
The new formula can be written as
The Wolfram screenshots to confirm above
Have a nice day !!
