SOLUTION: find the radical value of whole square root of 1+2 square root 1+3 square root 1+4 square root 1+...

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Question 1122159: find the radical value of
whole square root of 1+2 square root 1+3 square root 1+4 square root 1+...

Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!

As you show the problem, it makes no sense....

(1) The square root of 1 is 1; you are adding 1 a whole bunch of times, so the sum is going to be a whole number, not a radical.
(2) It appears to be an infinite arithmetic series, and has such it has no sum.

Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.
It is the "Ramanujan expression".

See relevant links and get fun

https://www.youtube.com/watch?v=9yMQMPj0zVU

https://www.youtube.com/watch?v=leFep9yt3JY

https://en.wikipedia.org/wiki/Nested_radical

http://mathworld.wolfram.com/NestedRadical.html

https://www.youtube.com/watch?v=r5BGIi84arY     ( * * ! * * )

The answer is "3".