Răspuns:
Explicație pas cu pas:
[tex]a)\f(x)=\frac{1}{x(x+1)}=\frac{x+1-x}{x(x+1)}=\frac{x+1}{x(x+1)}-\frac{x}{x(x+1)}=\frac{1}{x} -\frac{1}{x+1}\\\\b) S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{100}-\frac{1}{101}\\\\S=1-\frac{1}{101}=\frac{101-1}{101}=\frac{100}{101}[/tex]
