Let a1 be any real number, and let {an} be the sequencedefined recursively byan+1 = 12

Chapter 9, Problem 33

(choose chapter or problem)

Let  be any real number. and let \(\left\{a_{n}\right\}\) be the sequence defined recursively by

                    \(a_{n+1}=\frac{1}{2}\left(a_{n}+1\right)\)

Make a conjecture about the limit of the sequence, and confirm your conjecture by expressing \(a_{n}\) in terms of \(a_{1}\) and taking the limit.

Equation Transcription:

 

Text Transcription:

{a_n}

a_n+1=1/2(a_n+1)

a_n

a_1