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[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.

Janhaa 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.

$\sqrt{\frac{2}{2^2}+\sqrt{\frac{2}{2^4}+\sqrt{\frac{2}{2^8}+...}}}=\frac{1}{\sqrt{2}}\sqrt{\frac{2}{2^1}+\sqrt{\frac{2}{2^2}+\sqrt{\frac{2}{2^4}+...}}}=\frac{1}{\sqrt{2}}S$, så

$S=\sqrt{1+\frac{1}{\sqrt{2}}S}$, og

$S^2=1+\frac{1}{\sqrt{2}}S$ med positiv løsning $S=\sqrt{2}$.