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- Jan 26, 2012

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Various members (including myself) have shown this expression converges, and a few have expressed doubts about the existence of a closed form solution, but I was curious to see what the MHB community could come up with!

EDIT: huh! An analysis subforum popped into existence a few minutes ago. Can we move this there, please?

EDIT [Ackbach]: Your wish is my command.

EDIT: Thank you!

**algorithmshark**and not yet solved on math.stackexchange.com:He has posted some thoughts on his question: real analysis - Evaluating $\sqrt{1 + \sqrt{2 + \sqrt{4 + \sqrt{8 + \ldots}}}}$ - MathematicsEvaluate the following infinite radical:

$$\sqrt{1 + \sqrt{2 + \sqrt{4 + \sqrt{8 + \cdots}}}}$$

Various members (including myself) have shown this expression converges, and a few have expressed doubts about the existence of a closed form solution, but I was curious to see what the MHB community could come up with!

EDIT: huh! An analysis subforum popped into existence a few minutes ago. Can we move this there, please?

EDIT [Ackbach]: Your wish is my command.

EDIT: Thank you!

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