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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.
HistoryThese calculations were made by English mathematician John Wallis in 1640 and they formed the basis of differential calculus. |