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For $x\in R$ let [x] denote the greatest integer $\leq x$. Largest natural number $n$ for which

$E = [\pi/2]+[\pi/2+1/100]+[\pi/2+2/100]+[\pi/2+3/100]+\cdots+[\pi/2+n/100]<43$

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Well we know that $[\frac{\pi}{2}] = 1$. So, $n \leq 41$. Check that $[\frac{\pi}{2} + \frac{41}{100}] = 1$. So, $n= 41$.

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