wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> putnam exam (pure math) >> An inequality
        
(Message started by: acarchau on Dec 14^th, 2008, 9:48pm)

Title: An inequality
Post by acarchau on Dec 14^th, 2008, 9:48pm

Prove/disprove, for x>=0
(1+x)^(1+x) >= 1+x+x^2

Title: Re: An inequality
Post by towr on Dec 15^th, 2008, 1:38am

[hide]
take
f(x) = (1+x)^(1+x)
g(x) = 1+x+x^2
then
f(0)=g(0)
f'(0)=g'(0)
f''(x) >= g''(x) for x>=0
so (since they are continuous) f(x) >= g(x) for x>=0
[/hide]

Title: Re: An inequality
Post by ThudanBlunder on Dec 15^th, 2008, 3:30am

[hide]Binomial Theorem[/hide].