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Phidius (Posted on 2007-05-11) Difficulty: 3 of 5
Prove that

√(1+√(1+√(1+√(1+...))) = 1+1/(1+1/(1+1/(1+...)))

See The Solution Submitted by Jer    
Rating: 2.5000 (2 votes)

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Solution Solution Comment 4 of 4 |

Let:

v(1+v(1+v(1+v(1+...))) = p (say)......(i)
Or, 1+p = p^2
or, 1+ 1/p = p
Or, p 
= (1+ 1/p)
= (1+1/(1+ 1/p))
= (1+1/(1+ 1/(1+p))))
------------------------------------------------
-----------------------------------------------
= 1+1/(1+1/(1+1/(1+...))) ..........(ii)

Combining (i) and (ii), we obtain:

v(1+v(1+v(1+v(1+...))) = 1+1/(1+1/(1+1/(1+...)))

Edited on May 11, 2007, 2:33 pm
  Posted by K Sengupta on 2007-05-11 14:32:57

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