proof of bounds for e

Multiplying and dividing, we have


As was shown in the parent entry, the quotients in the product can be simplified to give


By the inequality for differences of powers,


Hence, we have the following upper bound:


By cross mutliplying, it is easy to see that


and, hence,


Factoring the rational function in the product, terms cancel and we have



Title proof of bounds for e
Canonical name ProofOfBoundsForE
Date of creation 2013-03-22 15:48:51
Last modified on 2013-03-22 15:48:51
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 4
Author rspuzio (6075)
Entry type Proof
Classification msc 33B99