Explicație pas cu pas:
[tex]log_{100}( \frac{1}{2} ) + log_{100}( \frac{2}{3} ) + ... + log_{100}( \frac{99}{100} ) = \\ [/tex]
[tex]= log_{100}( \frac{1}{2} \times \frac{2}{3} \times ... \times \frac{99}{100}) \\ [/tex]
[tex]= log_{100}( \frac{1}{100} ) \\ [/tex]
[tex]= log_{100}( {100}^{ - 1} ) = - 1[/tex]
