Question

Lg1/2+lg2/3+lg3/4+...+lg99/100

Answer 1

   
[tex]\displaystyle \text{Folosim formula:}\\ \lg a+\lg b=\lg(ab)\\\\ \lg\frac{1}{2}+\lg\frac{2}{3}+\lg\frac{3}{4}+\cdots +\lg\frac{99}{100}=\\\\ =\lg\left(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\cdots\times \frac{99}{100}\right)=\\\\ \text{Se fimplifica numitorul fracttiei (k) cu numaratorul fractiei (k+1) }\\\\ = \lg\left(\frac{1}{1}\times\frac{1}{1}\times\frac{1}{1}\times\cdots\times \frac{1}{100}\right)=\lg\frac{1}{100}=\lg\frac{1}{10^2}=\lg 10^{-2} = \boxed{-2}[/tex]