Originally Posted by

**Coop** Hi, I know the answer to the limit of this sequence but I am still unsure about the logic behind it.

So I am given a sequence sqrt(6), sqrt(6+sqrt(6)), sqrt(6+sqrt(6+sqrt6)))...

I know it is monotonic sequence, because it only increases.

So a(n+1)=sqrt(6+a(n))

And I can say that the lim(a(n+1))=lim(a(n)), right? Does that have to do it with it being monotonic?

Here is where I am confused, an answer key says to denote the limit as something, say L and put it into the equation

L = sqrt(6+L) (since the limits are equal)

Then you get L^2 - L - 6 = 0

And you get 3 as your answer, but why can you just put the limit (L) into the equation like that?