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Usenet Newsgroups : rec.puzzles Hall of Fame


The rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided.

Many of these puzzles also appear in Braingle's own collection.

   
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Categories : pickover : pickover.18.p

Title: Cliff Puzzle 18: Difficult Nested Roots
From: cliff@watson.ibm.com

If you respond to this puzzle, if possible please send me your name,
address, affiliation, e-mail address, so I can properly credit you if
you provide unique information.  PLEASE ALSO directly mail me a copy of
your response in addition to any responding you do in the newsgroup.  I
will assume it is OK to describe your answer in any article or
publication I may write in the future, with attribution to you, unless
you state otherwise.  Thanks, Cliff Pickover

      * * *

Consider the following nested set of square roots.

.eq ? = sqrt <1 + G sqrt <1+(G+1) sqrt < 1 + ... >>>

Here, G indicates "Googol" or  10**100.
The "<" and ">" symbols indicate where the beginning and ends of the
the nested roots.

1. What is the value for in this infinite set of nested roots.
2. What is the next term under the root?

Hint:
In 1911, the famous mathematical prodigy Srinivasa Ramanujan posed the
following question (#298) in a new mathematical journal called the
:Journal of the Indian Mathematical Society.

.eq ? = sqrt <1 + 2 sqrt <1+3 sqrt <1 + ... >>>



Solution


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