Induksjonsbevis
Moderators: Aleks855, Gustav, Nebuchadnezzar, Janhaa, DennisChristensen, Emilga
Regner med du kan bevise at dette holder for n=1 selv. Induksjonssteget som viser at det gjelder for n+1 gitt at det holder for n ligger ved her:
[tex]...+\frac{1}{n(n+1)}=\frac{n}{n+1}\Rightarrow ...+\frac{1}{n(n+1)}+\frac{1}{(n+1)(n+2)}=\frac{n}{n+1}+\frac{1}{(n+1)(n+2)}=\frac{n(n+2)+1}{(n+1)(n+2)}=\frac{n^2+2n+1}{(n+1)(n+2)}=\frac{n+1}{n+2}[/tex]
[tex]...+\frac{1}{n(n+1)}=\frac{n}{n+1}\Rightarrow ...+\frac{1}{n(n+1)}+\frac{1}{(n+1)(n+2)}=\frac{n}{n+1}+\frac{1}{(n+1)(n+2)}=\frac{n(n+2)+1}{(n+1)(n+2)}=\frac{n^2+2n+1}{(n+1)(n+2)}=\frac{n+1}{n+2}[/tex]