Find the limiting value of the sequence
A sequence is given by the recurrence relation:
$$u_n = 1 + {1\over u_{n-1} +1}, u_1 = 1, n{=\ge}1$$
Work out the 2nd, 3rd and 4th term of the sequence and find the limiting
value of the sequence.
So I worked out the first four terms are 1, $\frac32$, $\frac75$ and
$\frac{17}{12}$ and it looks like the sequence is an irrational number
1.41421...
Without recognising this is $\sqrt2$ just from being familiar with
1.4142... = $\sqrt2$ , is there any way to obtain $\sqrt2$ from the
recurrence relation?
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