Continued Square Root of 1, 2, 3, 4, .../Mistake

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Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary
$3$


Mistake

The value of the infinite nested root, $\sqrt {1 + \sqrt {2 + \sqrt {3 + \sqrt {4 + \cdots} } } }$ [equals $3$].


It is suspected that the given expression is a misprint for:

$\sqrt {1 + 2 \sqrt {1 + 3 \sqrt { 1 + \cdots} } }$

which famously equals $3$.


Also see


Sources