[tex]\displaystyle\\7)\\S=\lg\frac{1}{2} +\lg\frac{2}{3} +\lg\frac{3}{4} +\cdots +\lg\frac{99}{100}\\\\S=\lg\left(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times \cdots \times\frac{99}{100} \right)\\\text{Dupa simplificari avem:}\\\\S=\lg\left(\frac{1}{1}\times\frac{1}{100}\right)\\\\S=\lg\frac{1}{100}=\lg\frac{1}{10^2}=\lg10^{-2} = -2\\\\\boxed{\bf S=-2}[/tex]
