2. Zadatak

Zbroj $\frac a{1+a}+\frac b{1+b}+\frac c{1+c}+\frac d{1+d}+\frac e{1+e}$ možemo pisati redom $$\begin{aligned}&\frac a{1+a}+\frac b{1+b}+\frac c{1+c}+\frac d{1+d}+\frac e{1+e}=\frac{a+1-1}{1+a}+\frac{b+1-1}{1+b}+\frac{c+1-1}{1+c}+\frac{d+1-1}{1+d}+\frac{e+1-1}{1+e}\\&=\frac{1+a}{1+a}-\frac1{1+a}+\frac{1+b}{1+b}-\frac1{1+b}+\frac{1+c}{1+c}-\frac1{1+c}+\frac{1+d}{1+d}-\frac1{1+d}+\frac{1+e}{1+e}-\frac1{1+e}\\&=1-\frac1{1+a}+1-\frac1{1+b}+1-\frac1{1+c}+1-\frac1{1+d}+1-\frac1{1+e}\\&=5-\left(\frac1{1+a}+\frac1{1+b}+\frac1{1+c}+\frac1{1+d}+\frac1{1+e}\right)=5-\frac52=\frac52.\end{aligned}$$