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 June 26th, 2014, 09:59 AM #1 Newbie   Joined: Jun 2013 Posts: 5 Thanks: 0 Addition Solve the following problem. Root6 +( Root6 +(Root6+(Root6+(Root6 +……infinity. ) Here root means root over of till infinity.
 June 26th, 2014, 10:15 AM #2 Senior Member     Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 $sqrt{6+sqrt{6+sqrt{6+...}}}=n$ Square both sides: $6+sqrt{6+sqrt{6+sqrt{6+...}}}=n^2$ Substitute $sqrt{6+sqrt{6+sqrt{6+...}}}$ with n: $6+n=n^2$ Solve this quadratic equation: n=3 is the only positive.

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### solve root6 root6 ......infiniti

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