How much is 1√(1+ 2√(1+ 3√(1+ 4√(1+ 5√(...)))))? Does it tend to infinity?
Note: the initial 1 is just for completeness!
(In reply to
re: Solution by Googling by David Shin)
"I hope people understand that none of the previous posts came close to a solution."
Nor did the official "solution," except to mention Ramanujan, a solver in a class beyond compare!
The link I cited contains the reference
Aaron Herschfeld, AMM 42:7 (Aug.-Sept. 1935), pp. 419-429
which shows that the value of the expression we seek to evaluate depends on how we express the partial repeated square roots -- for example, a value of 4 instead of 3 can be obtained by using a less straightforward sequence of partial repeated square roots.
Ramanujan's solution is reproduced in Hardy's book of Collected papers of Ramanujan, page 323.
Edited on October 13, 2004, 7:21 pm
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Posted by Richard
on 2004-10-13 17:39:07 |
re(2): Solution by Googling
