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## Main Question or Discussion Point

I been trying to solve some nested radicals. I've been able to do:

[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

[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