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.
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?
P.S. If you don't get what my question is, I'd still appreciate your explanation on how to solve it.