Number e

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The value of the number e = 2.7182… can be calculated with the limit

We calculate the limit with simple numbers, and start with n = 1, that gives

Now we take n = 2, and get

That is somewhat more. Further with n = 3, to find out if this continues so nicely

The value increases steadily. We try also n = 100 and obtain

If we continue, you will notice that the first place after the decimal point doesn't change anymore. In this way we get the required accuracy

In 1683 the Swiss mathemarician Jacob Bernoulli discovered this constant by studying compound interests.