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Infinite series

People have always been amazed that some infinite series give an exact solution.

 


Calculations

A simple set without powers

The same series with 2nd powers

The same series with 3rd powers

You can guess what the outcome will be of the same suit with 4th powers

Try to find a formula for the latter term where n is used. The numerator increases much slower than the denominator, and eventually the value of the fraction will become zero.

 


Additional information

These calculations were made by John Wallis in 1640 and they formed the basis of differential calculus.

 


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