Due December 20

This problem requires that you make a small mental leap to the end of an infinite sequence. We consider this to be a hard problem, worth 20 points. Send answers and questions to mathstat@uoguelph.ca

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.

StepNumber
01
12=1/1+1
21.5=1/2+1
31.666666667=1/1.5+1
41.6
51.625
61.615384615
71.619047619
81.617647059
91.618181818
......

Hint: the answer involves a square root which you can e-mail as SQRT. So if the answer were one minus the square root of three all over seven you could e-mail me (1-SQRT(3))/7. You can also e-mail me a scan of your work.

Send your answer to mathstat@uoguelph.ca

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