I was going through a list of important Mathematical Constants, when I saw the Khinchin's constant.
It said that :
If a real number r is written as a simple continued fraction :
r=a0+1a1+1a2+1a3+…, where ak are natural numbers ∀k, then lim exists and is a constant K \approx 2.6854520010, except for a set of measure 0.
First obvious question is that why the value a_0 is not included in the Geometric Mean? I tried playing around with terms and juggling them but was unable to compute the limit. Also, is it necessary for r to be "written-able" in the form of a continued fraction ?
Thanks in Advance ! :-)
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