Very pleasing puzzle from Dan Asimov:

Define a function f : [0,∞) → ℝ via

\[ f(x) = \sqrt{1+x\sqrt{1+(x+1)\sqrt{1+(x+2)\sqrt{1+\ldots}}}} \]

Evaluate f(x) in closed form.

@ColinTheMathmo I should put some kind of scrolling on maths in toots.

@christianp Would that be hard?

@ColinTheMathmo nah, just a CSS rule

@christianp @ColinTheMathmo CSS is my very definition of "hard". Browser compat means the rules can change depending on who's looking at it. I mean imagine if the + sign was what some countries used for a -.

@jsmall @christianp There is a little of that - in France they think that 0 is both positive *and* negative.

ColinTheMathmo@ColinTheMathmo@mathstodon.xyz@christianp Can't see the entire expression, need to comment to see the raw LaTeX in the text.

But ... hmmm ...