Napier's constant
The value of the number e = 2,7182… can be calculated with the limit
Explanation
We use the binomium development
As it was a limit, we can write
If we apply several times l'Hôpita'ls rule on the different terms, we get
The subsequent terms give then
1 = 1.0000
1/1! = 1.0000
1/2! = 0.5000
1/3! = 0.1667
1/4! = 0.0417
1/5! = 0.0083
1/6! = 0.0014
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e = 2.718…
HistoryThe name is a tribute to the Scottish mathematician John Napier (1550 - 1617), who calculated the natural logarithms. |