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I was wondering how to find the value of the following series:

$$\cfrac{1}{2+\cfrac{1}{3+\cfrac{1}{4+\cfrac{1}{5+\cfrac{1}{6+\ddots}}}}}$$

How can I solve this?

Michael Hardy
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AMACB
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  • It equals $$\frac{I_0(2)}{I_1(2)}-1 = 0.43312742672231\ldots $$ where $I_k$ are modified Bessel functions of the first kind. – Jack D'Aurizio Sep 06 '16 at 23:39
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    Incidental question ... what search in the math.se search box would have found that duplicate question? – GEdgar Sep 07 '16 at 00:31

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