Apery Constant and Consecutive Numbers

Roger Apery stunned the whole world when he considered the Riemann-Zeta function for 3. He moreover proved the irrationality and stated transcendental properties for zeta(3).

The Riemann zeta function for 3 is now called Apery constant, honoring him. The value of Apery Constant is 1.2020569 . . . . 

Now, with the help of Wolfram Alpha, I combined the concept of Apery constant and consecutive numbers. And have made the following statement.

I hope you like the above expression.

Have a nice day !!