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

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