bounds for e

If n and m are positive integers and n>m, we have the following inequalityMathworldPlanetmath:


Taking the limit as n, we obtain an upper boundMathworldPlanetmath for e. Combining this with the fact that the (1+1/n)n is an increasing sequence, we have the following bounds for e:


This can be used to show that e is not an integer – if we take m=5, we obtain 2.48832<e<2.985984, for instance.

Title bounds for e
Canonical name BoundsForE
Date of creation 2013-03-22 15:48:48
Last modified on 2013-03-22 15:48:48
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 7
Author rspuzio (6075)
Entry type Theorem
Classification msc 33B99