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

Source Work

 * The Dictionary
 * $3$
 * $3$

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

 * Ramanujan's Infinite Nested Roots