Expressions of the form

Herschfeld (1935) proved that a continued square root of Real Nonnegative terms converges Iff is bounded. He extended this result to arbitrary Powers (which include continued square roots and Continued Fractions as well), which is known as Herschfeld's Convergence Theorem.

**References**

Herschfeld, A. ``On Infinite Radicals.'' *Amer. Math. Monthly* **42**, 419-429, 1935.

Pólya, G. and Szegö, G. *Problems and Theorems in Analysis, Vol. 1.* New York: Springer-Verlag, 1997.

Sizer, W. S. ``Continued Roots.'' *Math. Mag.* **59**, 23-27, 1986.

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1999-05-26