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wu :: forums    riddles    putnam exam (pure math) (Moderators: Eigenray, Grimbal, towr, Icarus, SMQ, william wu)    Factorials « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Factorials  (Read 456 times) ThudnBlunder Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Factorials   « on: Dec 6th, 2004, 12:21am » Quote Modify Let  m  and  n  be positive integers.     Show that   (m+n)! /  (m+n)(m+n)  <  (m!)*(n!)  /  [(mm) * (nn)]   IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Aryabhatta Uberpuzzler     Gender: Posts: 1321 Re: Factorials   « Reply #1 on: Dec 9th, 2004, 2:16am » Quote Modify The following works: Rearrange as (m+n)!*(m^m)*(n^n)/(m!)*(n!) < (m+n)^(m+n) and using binomial theorem makes it almost trivial.   A week away from this forum and wow! So many new puzzles... nice. Should go away more often     IP Logged 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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