[VA] Short & Sweet Math Challenge #25 "San Valentin's Special: Weird Math"

[J-F Garnier]

(02-19-2021 11:32 PM)Valentin Albillo Wrote:  Concoction the Second: Weird Sum

      The main question is wholly unaddressed: What's so weird about this sum ?. Perhaps a little sleuthing (i.e.: conducting some experiments) would be of help.

I can't explain how this sum converges to 1/2021.
I tried other constant value than 2021, it still worked.

Then I asked myself: are the prime numbers the key for the convergence?
So I calculated the terms, using the suite of natural integers instead of the primes.

1 x 2 x 3 x 4 x 5 x ... (n-1)
--------------------------------
(A+2) x (A+3) x (A+4) x ... (A+n)

Where A is the constant, 2021.

10 A=2021 @ S=0 @ X=1
20 FOR I=1 TO 10
30 X=X*I/(A+I+1) ! next term
40 S=S+X ! sum
50 NEXT I
60 DISP S, 1/S

And guess what? The sum seems to still converge to 1/A

Quite weird, no?

J-F