Răspuns:
[tex]\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+...+\frac{1}{100*101}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{100} -\frac{1}{101}=\frac{1}{1}-\frac{1}{101}= \frac{101}{101}-\frac{1}{101}=\frac{100}{101} \\Deci~\frac{100}{101}=\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+...+\frac{1}{100*101}.[/tex]
Explicație pas cu pas:
este o suma de 100 termeni.
