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wu :: forums    riddles    putnam exam (pure math) (Moderators: william wu, Eigenray, towr, SMQ, Icarus, Grimbal)    An inequality « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: An inequality  (Read 1067 times) acarchau Newbie     Posts: 3 An inequality   « on: Dec 14th, 2008, 9:48pm » Quote Modify Prove/disprove, for x>=0   (1+x)^(1+x) >= 1+x+x^2 IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: An inequality   « Reply #1 on: Dec 15th, 2008, 1:38am » Quote Modify 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   IP Logged Wikipedia, Google, Mathworld, Integer sequence DB ThudnBlunder Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: An inequality   « Reply #2 on: Dec 15th, 2008, 3:30am » Quote Modify Binomial Theorem. IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs => putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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