Bernoulli Inequality

Author

Eric W. Weisstein
April 13, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/BernoulliInequality.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BernoulliInequality.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Inequality

FullSimplify[(1+x)^a>=1+a x,Assumptions->#]&/@{a<0,0<a<1,a>1}

Refine[(1+x)^a>=1+a x,Assumptions->#&&x>-1]&/@{a<0,0<a<1,a>1}

Reduce[(1+x)^a>=1+a x&&#&&x>-1,{}]&/@{a<0,0<a<1,a>1}

...hangs...

Reduce[(1+x)^a>=1+a x&&#&&x>-1]&/@{a<0,0<a<1,a>1}

...hangs...

Resolve[(1+x)^a>=1+a x&&#&&x>-1]&/@{a<0,0<a<1,a>1}