I have made a formula for 2n factorial. I have called it the devil formula because 3.3 can be 3 or 3.33333 . Similarly 0.066 can be 0.06 or 0.0666. And so can 1.3 be 1.33 or 1.3333. This formula can be adjusted and near value of 2n factorial be reached. However this formula works from 100 to above.
The formula is
Hope you have a fine day !!
You may be aware that I made 2n! formula of the type ((((n+1)(n+2))/2)^(n)). I have made it very approximate.
The formula for (2n)! is
The Wolfram Alpha results to confirm that the formula is now very approximate.
Have a nice weekend!!
(Today on September 8th, 2024)
If you are doing a programming in computer, then you may use the following. The results will be more accurate.
I have been working on ((((n+1)(n+2))/2)^n) since April. 5 months. I derived the formula from Measuring Behavior expression or what I term it to be equivalent to Wallis pi. I was trying to get 0.5 factorial. While doing that I discovered the above pattern for (2n)!. So a journey of 5 months of intense application ended yesterday night.
Of course, James Stirling formula for n! is far more superior and has far more fidelity.
But the expression (((n+1)(n+2))/2) is the sum of first (n+1) numbers. And that is the reason why I persisted with this formula. Because sum of (n+1) numbers to the power n is related to 2n!. I found that interesting!!
I was not sure whether two of my approximations statements were true or not.
They were
(a/b)^k
the next numbers
Math GPT has done analysis and found out that the statements are true
(a/b)^k
the next numbers
I am feeling satisfied. Have a nice day !!
