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
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3$