Question

Sequences/Series help. *Question attached below* Will give medal

Answer 1

So I've been trying to do this question for the past hour and still can't find out where to start. Can someone explain to me how I should start tackling this?

Answer 2

may or may not be correct not sure.
\[\lim_{n \rightarrow \infty}x _{n}=\lim_{n \rightarrow \infty} x _{n+1}=l\]
\[x _{n+1}=\sqrt{5+x _{n}},\]
taking limits as
\[as~n \rightarrow \infty ,l=\sqrt{5+l},or~l^2-l-5=0\]

Answer 3

How did you arrive at the last line?

Answer 4

squaring
\[x _{n+1}*x _{n+1}=5+x _{n}\]
now take the limits as \(~n rightarrow infinity\)

Answer 5

Thank you!