matematikk.net

[tex]\log \left( \frac{1}{2} \right) + \log\left( \frac{2}{3} \right) + \log\left( \frac{3}{4} \right) + \,...\, + \log\left( \frac{97}{98} \right) +\log\left( \frac{98}{99} \right) +\log\left( \frac{99}{100} \right) =[/tex]

Teleskoprekke.

[tex]\log\left(\frac ab\right)=\log a-\log b \\ \log(1)-\log(2)+\log(2)-\log(3)+\log(3)...-\log(100)=\log(1)-\log(10)=-\log(100)=-2[/tex]

eventuelt

[tex]\log(ab)=\log(a)+\log(b)[/tex]
[tex]\log\left(\frac{99!}{100!}\right)=\log\left(\frac{1}{100}\right)=-\log(100)=-2[/tex]