Question

Va rog eu mult,urgent!!!!

Answer 1

Răspuns:

Explicație pas cu pas:

$a=(2+4+6+...+4022)*(\frac{1}{1*2}+ \frac{1}{2*3}+\frac{1}{3*4}+\frac{1}{4*5}+...+\frac{1}{2010*2011}+\frac{1}{2011*2012})=2*(1+2+3+...+2011)*(\frac{1}{1}-\frac{1}{2}+ \frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2010}-\frac{1}{2011}+\frac{1}{2011}-\frac{1}{2012})=2*\frac{2011*(2011+1)}{2}*(1-\frac{1}{2012})=2011*2012*\frac{2011}{2012}=2011*2011=2011^{2}, ~patrat~ perfect$