[tex]S=\sqrt{\frac{2}{2^1}+\sqrt{\frac{2}{2^2}+\sqrt{\frac{2}{2^4}+\sqrt{\frac{2}{2^8}+...}}}}[/tex]
Hva er summen lik?
Ite'no Wolfram juks.
summen
Moderatorer: Vektormannen, espen180, Aleks855, Solar Plexsus, Gustav, Nebuchadnezzar, Janhaa
$\sqrt{\frac{2}{2^2}+\sqrt{\frac{2}{2^4}+\sqrt{\frac{2}{2^8}+...}}}=\frac{1}{\sqrt{2}}\sqrt{\frac{2}{2^1}+\sqrt{\frac{2}{2^2}+\sqrt{\frac{2}{2^4}+...}}}=\frac{1}{\sqrt{2}}S$, såJanhaa skrev:[tex]S=\sqrt{\frac{2}{2^1}+\sqrt{\frac{2}{2^2}+\sqrt{\frac{2}{2^4}+\sqrt{\frac{2}{2^8}+...}}}}[/tex]
Hva er summen lik?
Ite'no Wolfram juks.
$S=\sqrt{1+\frac{1}{\sqrt{2}}S}$, og
$S^2=1+\frac{1}{\sqrt{2}}S$ med positiv løsning $S=\sqrt{2}$.