The simple continued fraction is both the most interesting and important kind of continued fraction.
Similarly the continued fraction given by Euler as equivalent to (e - 1) (e being the base of Napierian logarithms), viz.
There is, however, a different way in which a Series may be represented by a continued fraction.
For the convergence of the continued fraction of the second class there is no complete criterion.
He had not then the continued fraction, a mode of representation which he gave the next year in his work on the square root.
If a or b is unity, a/b cannot be converted into a continued fraction with unit numerators, and the above method fails.
The continued fraction is therefore incommensurable, and cannot be unity.