need explanation for integer part

Dec 2015
1,082
169
Earth
Is this statement true ? \(\displaystyle \lfloor n/2 \rfloor \approx \frac{n}{2}+ \frac{1-(-1)^n }{4}\). \(\displaystyle \; n\in \mathbb{N}\) and \(\displaystyle n\neq 1\).
 
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romsek

Math Team
Sep 2015
2,958
1,673
USA
not quite

$\left \lfloor \dfrac n 2 \right\rfloor = \dfrac n 2 - \dfrac{1-(-1)^n}{4}$
 
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