Start with the number 1 and repeat the following two steps many
times: compute the reciprocal and then add one. The first few steps
(rounded in some cases) are shown below. This sequence settles down
to a specific, and moderately famous, number. The question: find it's
exact value.
Step  Number 

0  1 
1  2=1/1+1 
2  1.5=1/2+1 
3  1.666666667=1/1.5+1 
4  1.6 
5  1.625 
6  1.615384615 
7  1.619047619 
8  1.617647059 
9  1.618181818 
...  ... 
Hint: the answer involves a square root which you can email as
SQRT. So if the answer were one minus the square root of three all
over seven you could email me (1SQRT(3))/7. You can also email me
a scan of your work.
Send your answer to mathstat@uoguelph.ca
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