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

 October 18th, 2019, 10:38 AM #1 Senior Member   Joined: Dec 2015 From: Earth Posts: 826 Thanks: 113 Math Focus: Elementary Math need explanation for integer part Is this statement true ? $\displaystyle \lfloor n/2 \rfloor \approx \frac{n}{2}+ \frac{1-(-1)^n }{4}$. $\displaystyle \; n\in \mathbb{N}$ and $\displaystyle n\neq 1$. Last edited by idontknow; October 18th, 2019 at 10:51 AM. October 18th, 2019, 10:54 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,638 Thanks: 1475 not quite $\left \lfloor \dfrac n 2 \right\rfloor = \dfrac n 2 - \dfrac{1-(-1)^n}{4}$ Thanks from topsquark and idontknow October 19th, 2019, 02:50 AM #3 Senior Member   Joined: Dec 2015 From: Earth Posts: 826 Thanks: 113 Math Focus: Elementary Math Also $\displaystyle (-1)^n =e^{i\pi n} =4\lfloor n/2 \rfloor -2n+1$. Now the integer part can be expressed as infinite series . Floor Function -- from Wolfram MathWorld Last edited by idontknow; October 19th, 2019 at 03:03 AM. October 19th, 2019, 06:17 AM   #4
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Math Focus: Elementary Math
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 Originally Posted by idontknow Also $\displaystyle (-1)^n =e^{i\pi n} =4\lfloor n/2 \rfloor -2n+1$. Now the integer part can be expressed as infinite series . Floor Function -- from Wolfram MathWorld
My essence was to express (-1)^n in one single equality using integer parts . Tags explanation, 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 idontknow Number Theory 12 May 13th, 2019 01:35 PM idontknow Elementary Math 3 January 19th, 2019 05:56 AM Dacu Algebra 7 April 17th, 2015 06:05 AM Albert.Teng Algebra 2 September 23rd, 2012 04:46 AM Fernando Number Theory 1 April 13th, 2012 07:19 AM

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