I been trying to solve some nested radicals. I've been able to do:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\[\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}\][/tex]

Which is pretty cool since it equals to the "Golden Ratio" or [tex]\[\frac{\sqrt{5}+1}{2}\][/tex]

But I can't seem to do the following:

[tex]\[\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\cdots}}}}\][/tex]

Using a calculator, it seems that this converges to [tex]$\sqrt{3}$[/tex]. Could anyone show me how? Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Nested Radicals

**Physics Forums | Science Articles, Homework Help, Discussion**