Zeta(2) or Basel Problem or pi squared by 6

This problem was called Basel Problem. Bernoulli posed this problem. Leonhard Euler, a young man in his twenties proved it. It was a phenomenon in mathematical circles. Euler earned fame. He was called by the King of Prussia himself. He made mathematical theories due to which he is called 'King of Mathematics'. He has left so many theories that not all of them have been comprehended. He slowly began to loose his eyesight. But not his mathematical insights. Leonhard Euler was so great.

So Zeta(2) or Basel Problem or pi squared by 6 is given below as computed by consecutive numbers.

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Zeta(3)

Zeta(3) which is Apery constant is calculated by consecutive numbers. I thought 1/n^2 and n/(n+1)^3 will be calculated separately but not.

The following is zeta(3).

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Zeta(7)

 The zeta(7) expression with consecutive numbers is given below

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Zeta(5)

Zeta(5) is now well expressed with consecutive numbers.

Below is the expression

And Wolfram Alpha screen to confirm the above.

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Art Issues

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.

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Objectives in drawing art

 

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