- #1

- 48

- 0

This is the series:

[tex]\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5...}}}}}[/tex]

Any thoughts would be very much appreciated.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter PEZenfuego
- Start date

- #1

- 48

- 0

This is the series:

[tex]\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5...}}}}}[/tex]

Any thoughts would be very much appreciated.

- #2

Char. Limit

Gold Member

- 1,208

- 14

Wolfram Mathworld said:Herschfeld (1935) proved that a nested radical of real nonnegative terms converges iff [tex]x_n^{2^{-n}}[/tex] is bounded.

So, the question is, is x

[tex]f(n)=n^{2^{-n}}[/tex]

And we find that indeed, this function is bounded. So yes, your nested radical is convergent.

- #3

- 129

- 0

[tex]\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5...}}}}}\approx 1.7579327566180045327[/tex]

Share: