E = $\frac{\left( 2-\frac{2}{3} \right)\times \left( 3-\frac{3}{4} \right)\times \left( 4-\frac{4}{5} \right)\times .....\times \left( 999-\frac{999}{1000} \right)}{3\times 4\times 5\times ....\times 1000}$

$E=\frac{\frac{4}{3}\times \frac{9}{4}\times \frac{16}{5}\times ...\times \frac{998001}{1000}}{3\times 4\times 5\times ...\times 1000}$

$E=\frac{4\times 9\times 16\times ...\times 998001}{3\times 4\times 5\times ...\times 1000}\times 3\times 4\times 5\times ...\times 1000$

$E=4\times 9\times 16\times ...\times 998001>1$