Question

am nevoie repede
Va rog ajutor​

Answer 1

Explicație pas cu pas:

$A = \lg\Big(\dfrac{1}{2} \Big) + \lg\Big(\dfrac{2}{3} \Big) + \lg\Big(\dfrac{3}{4} \Big) + ... + \lg\Big(\dfrac{99}{100} \Big) =$

$= \lg\Big(\dfrac{1}{ \not2} \cdot \dfrac{\not2}{\not3} \cdot \dfrac{\not3}{\not4} \cdot ... \cdot \dfrac{\sout{99}}{100} \Big) = \lg \Big(\dfrac{1}{100} \Big)$

$= \log_{10} \Big(\dfrac{1}{10^{2}} \Big) = \log_{10} 10^{- 2} = - 2$