Explicație pas cu pas:
[tex]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) = \\ [/tex]
[tex]= \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)[/tex]
[tex]= \log_{10} \Big(\dfrac{1}{10^{2}} \Big) = \log_{10} 10^{- 2} = - 2[/tex]
Show life that you have a thousand reasons to smile
© Copyright 2024 DOKU.TIPS - All rights reserved.
Verified answer
Explicație pas cu pas:
[tex]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) = \\ [/tex]
[tex]= \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)[/tex]
[tex]= \log_{10} \Big(\dfrac{1}{10^{2}} \Big) = \log_{10} 10^{- 2} = - 2[/tex]