PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (194)
Orphanage
Unclass'd
Unproven (498)
Corrections (25)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Very high Entry average rating: No information on entry rating
Bernoulli's inequality (Theorem)

Let $ x$ and $ r$ be real numbers. If $ 0>r>-1$ or $ r>1$ and $ x>-1$ then

$\displaystyle (1+x)^r\ge 1+xr.$

The inequality also holds when $ r$ is an even integer. For $ 0<r<1$ the inverse inequality holds.



"Bernoulli's inequality" is owned by rspuzio. [ full author list (2) | owner history (2) ]
(view preamble)

View style:

See Also: inequalities for differences of powers


Attachments:
proof of Bernoulli's inequality (Proof) by danielm
another proof of Bernoulli's inequality (Proof) by a4karo
proof of Bernoulli's inequality employing the mean value theorem (Proof) by rspuzio
Log in to rate this entry.
(view current ratings)

Cross-references: inverse, even integer, inequality, real numbers
There are 2 references to this entry.

This is version 6 of Bernoulli's inequality, born on 2001-10-17, modified 2006-06-08.
Object id is 275, canonical name is BernoullisInequality.
Accessed 10530 times total.

Classification:
AMS MSC: 26D99 (Real functions :: Inequalities :: Miscellaneous)
Pending Errata and Addenda
None.
[ View all 5 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | prove | add result | add corollary | add example | add (any)