(a) Given that and , show that
is convergent and .
(b) Let and Write out the first
eight terms of . Use part (a) to show that .
This gives the continued fraction expansion
To prove: The sequence is convergent and .
The limit values of sequence are, and .
The limit can be written as: .
Consider the sequence .
If is a bound below for , that is for all n,
So, is bounded above.
Also, it can be seen that that that is .
Therefore, the converges to some limit L by the monotone convergence theorem.
Thus, the limit law sequence is also converges to .
Let, be given. means there exists such that for
To calculate: The first eight terms of sequence .
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