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 March 6th, 2018, 12:10 PM #1 Senior Member   Joined: Dec 2015 From: Earth Posts: 820 Thanks: 113 Math Focus: Elementary Math Show inequality true Show that $\displaystyle (1+ \frac{1}{n} )^n < (1+ \frac{1}{n+1})^{n+1} \;$ for $\displaystyle n$ natural March 6th, 2018, 01:48 PM #2 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,974 Thanks: 1156 Math Focus: Elementary mathematics and beyond Make an attempt and post your work. Are you expected to use any particular method, such as induction? March 8th, 2018, 01:21 PM #3 Senior Member   Joined: Dec 2015 From: Earth Posts: 820 Thanks: 113 Math Focus: Elementary Math Since $\displaystyle (1+\frac{1}{n})^n=f(n)1$ use Bernoulli's inequality $\displaystyle (1+r)^x>1+xr$ with conditions $\displaystyle [1+(-(n+1)^{-2}))]^{1+n}>1+(-(n+1)^{-2}\Rightarrow (1+\frac{1}{n})^n < (1+\frac{1}{n+1})^{n+1}$ Tags inequality, show, true 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 honzik Applied Math 1 September 30th, 2016 02:28 AM Lucida Algebra 10 March 26th, 2012 05:16 PM Anton29 Calculus 2 November 29th, 2011 10:18 PM 450081592 Advanced Statistics 6 October 27th, 2011 07:28 PM fc_groningen Advanced Statistics 4 January 23rd, 2011 02:03 AM

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