An Expression For e

The number e=2.718281828 is the base of the natural log.occurs in many areas of maths, and there are many methods to calculate it. One such is as the limit of the sequenceastends to infinity.

 n $(1 + 1/n)^n$ 1 2 2 2.25 3 2.370370370 4 2.44140625 10 2.593742460 100 2.704813829 1000 2.716923932 10000 2.718145927 100000 2.718268237

The table shows that asgets largergets closer toWe can write

Writewhereis a fixed number.

so that as n tends to infinityThe solution to this differential equation isso putto obtain

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