Question

Sper sa primesc rezultatul la ex. 7. Din aceea imagine.

Answer 1

 

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

Answer 2

S=lg (1\2 ·2\3 ·3\4 ·...·99\100) = lg (1\100) =log 10 (10 la -2) =-2 >= S=-2 .