Thursday, August 04, 2005

Today's quickie math puzzle, Thu, Aug 4.


What is the value of sqrt(2 + sqrt(2 + sqrt(2 + ... )))? Open for solutions now.

3 comments:

Jon Dursi said...

Ok, this one I think I can get. The answer is 2.

s = sqrt(2 + sqrt(2 + sqrt(2+...)))

s^2 = 2 + sqrt(2 + sqrt(2 + sqrt(2+...)))

s^2 = 2 + s

s^2 - s - 2 = 0

s = 2, -1

The negative root makes no sense in this case, leaving s = 2.

Jon Dursi said...

Hey, how come your trolls never seem to post on these threads? Mathematical reasoning is a little intimidating, I suppose.

CC said...

There is a slightly simpler way to look at it as well and that is to notice that, if you let "s" be the solution, then:

s = sqrt(2 + s)

The answer falls out of that pretty quickly.