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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 January 18th, 2019, 07:49 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 728 Thanks: 98 Integer part How can I find the integer part of $\displaystyle e^e \;$? (without calculator) e - Euler constant What about approximation? First, I tried one example for $\displaystyle 2e$ and $\displaystyle e^2$, to see whether it is possible. $\displaystyle 3>e>\frac{5}{2}\;$ ,then multiply by 2 6>2e>5 so integer part of 2e is 5. Last edited by skipjack; January 18th, 2019 at 11:21 PM. January 18th, 2019, 11:27 PM #2 Global Moderator   Joined: Dec 2006 Posts: 21,028 Thanks: 2259 How much basic arithmetic is acceptable, given that use of a calculator isn't allowed? Can you assume that e = 2.718... or does that have to be proved as well? January 19th, 2019, 01:01 AM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 728 Thanks: 98 By calculator ,integer part of $\displaystyle e^e$ is 15. But integer part of $\displaystyle {2.7}^{2.7}$ is 14 , same for 2.71 . Last edited by idontknow; January 19th, 2019 at 01:07 AM. January 19th, 2019, 04:56 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,028 Thanks: 2259 $e^{2.71} >15$, but I think a lot of arithmetic is needed to prove that. Tags integer, part Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Dacu Algebra 7 April 17th, 2015 05:05 AM gerva Algebra 18 January 6th, 2015 06:38 AM Jakarta Number Theory 0 May 12th, 2013 10:09 AM Albert.Teng Algebra 2 September 23rd, 2012 03:46 AM Fernando Number Theory 1 April 13th, 2012 06:19 AM

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