
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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September 7th, 2019, 01:34 PM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 827 Thanks: 113 Math Focus: Elementary Math  Equation with natural variable
$\displaystyle \lfloor n/1 \rfloor + \lfloor n/2 \rfloor +...+\lfloor n/(n1) \rfloor =7\; $, nnatural . To write it better : $\displaystyle \sum_{j=1}^{n1} \displaystyle \lfloor \frac{n}{j} \displaystyle \rfloor =7 \; $ ; n=? , Method Required ! Last edited by idontknow; September 7th, 2019 at 01:38 PM. 
September 8th, 2019, 03:27 AM  #2 
Senior Member Joined: Dec 2015 From: Earth Posts: 827 Thanks: 113 Math Focus: Elementary Math 
$\displaystyle m_1 =\lfloor 7/2 \lfloor $ and $\displaystyle m_{2} =1+m_1 $. $\displaystyle M=\frac{1+2m_1 }{2}=3,5$. Number of elements is $\displaystyle \lfloor 3,5 \rfloor =3 $ which is n+1 .So $\displaystyle n=4$. To verify : [4]+[4/2]+[4/3] =4+2+1=7 . 

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