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

$E=\left[\frac{\pi }{2}\right]+\left[\frac{1}{100}+\frac{\pi }{2}\right]+\left[\frac{2}{100}+\frac{\pi }{2}\right]\dots +\left[\frac{n}{100}+\frac{\pi }{2}\right]<43,$ is

Since $3.14<\pi <3.142,1.57<\pi /2<1.571$
Thus, $\left[\frac{\pi }{2}+\frac{n}{100}\right]=1$for $n=0, 1, 2,......, 42$
Thus, largest natural number $n$ for which $E<43$ is $41.$