Răspuns:
lg1/2=lg1-lg2
lg2/3=lg2-lg3
...........................
lg9/10=lg9-lg10
-----------------------se aduna membru cu membru
lg1/2+lg2/3+...+lg9/10=lg1-lg2+lg2-lg3+....+lg9-lg10=0-0+....+0-1=
=-1
Explicație pas cu pas:
[tex]\displaystyle \lg\frac{1}{2}+\lg\frac{2}{3}+\lg\frac{3}{4}...+\lg\frac{9}{10}= \\ \\ =\lg\Big(\frac{1}{2}\cdot \frac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot \frac{8}{9}\cdot \frac{9}{10}\Big) = \\ \\ = \lg\Big(\dfrac{1}{10}\Big) = \lg 10^{-1} =-\lg 10 = -1[/tex]
