Răspuns:
Explicație pas cu pas:
[tex]\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+...+\frac{1}{99*100}+\frac{1}{100*101} =\frac{1}{1} -\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+ \frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}+\frac{1}{100}-\frac{1}{101}=\frac{1}{1}-\frac{1}{101}=\frac{101}{101}-\frac{1}{101}=\frac{100}{101} .[/tex]
