
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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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 $\left \lfloor \dfrac n 2 \right\rfloor = \dfrac n 2  \dfrac{1(1)^n}{4}$ 
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  
Senior Member Joined: Dec 2015 From: Earth Posts: 826 Thanks: 113 Math Focus: Elementary Math  Quote:
 

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