Răspuns:
n
Explicație pas cu pas:
[tex]\frac{2}{n+1} + \frac{4}{n+1} + \frac{6}{n+1} + .... + \frac{2n}{n+1} =[/tex]
[tex]= 2(\frac{1}{n+1} + \frac{2}{n+1} + \frac{3}{n+1} + .... + \frac{n}{n+1} ) =[/tex] (am dat factor comun pe 2)
[tex]= 2(\frac{1+2+3+ .... + n}{n+1} ) =[/tex]
[tex]= 2 \frac{\frac{n(n+1)}{2} }{n+1} = 2\frac{n(n+1)}{2} \frac{1}{n+1}[/tex] - am folosit formula 1+2+...n = n(n+1):2
= n
