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A simple proof of Euler's continued fraction of <i>e</i><sup>1/<i>M</i></sup>

A simple proof of Euler's continued fraction of <i>e</i><sup>1/<i>M</i></sup>

A continued fraction is an expression of the form and we will denote it by the notation [ f 0 , ( g 0 , f 1 ), ( g 1 , f 2 ), ( g 2 , f 3 ), … ]. If the numerators g i are …