combination(2n,n) from consecutive numbers

I have managed to get combination(2n,n) from consecutive numbers. Here is the formula

Here are the Wolfram screenshots to confirm the above.

So what do we have

1. Consecutive numbers form as sigma gives constants and other numbers.

2. consecutive numbers in products gives combination(2n,n)

3, combination(2n,n) gives constants and other expressions

4. consecutive numbers in another form gives rise to binomials.

5. binomials of form from above gives approximations and other results.

That's all folks. Planning to give up mathematics endeavor from now onwards. Nothing more is left out. Knitted a good theory in above.

I shall check Academia app and try and look for mathematics of Gauss, Euler, Ramanujan and Abel.

My good wishes. Have a nice day !!