# Monotonic Convergence to $$e$$ via the Arithmetic-Geometric Mean

Hansheng Yang and Heng Yang used the arithmetic-geometric mean inequality to prove that the sequence $$[1+1/n]^n$$ is monotonic increasing converging to $$e$$ whereas $$[1+1/n]^{n+1}$$ is monotonic decreasing converging to $$e$$. The author provides a simpler proof using the same technique.

Old Node ID:
3666
MSC Codes:
26A03
Author(s):
Józef Sáandor (Babes-Bolyai University Romania)
Publication Date:
Monday, April 25, 2011
Original Publication Source:
Mathematics Magazine
Original Publication Date:
June, 2007
Subject(s):
Calculus
Single Variable Calculus
Limits
Topic(s):
Approximations: pi, e, natural logarithms
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Rating Count:
20.00
Rating Sum:
63.00
Rating Average:
3.15
Applicable Course(s):
3.1 Mainstream Calculus I
Modify Date:
Friday, August 17, 2012