Question

Calculați: (1-1/2)x(1-1/3)x(1-1/4)x…x(1-1/2011) VA ROG!

Answer 1

$\bigg(1 - \frac{1}{2}\bigg)\bigg( 1 - \frac{1}{3}\bigg )\cdot\ldots\cdot\bigg( 1 - \frac{1}{2011}\bigg ) \\ \\ = \frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdot \frac{4}{5} \cdot\ldots\cdot \frac{2010}{2011} \\ \\ = \frac{1}{2011}$

Se simplifică 2 cu 2; 3 cu 3; 4 cu 4..... 2010 cu 2010.