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The proof is straightforward. From the fraction itself, one can construct the quadratic equation with integral coefficients that x must satisfy. Lagrange proved the converse of Euler's theorem: if x is a quadratic irrational, then the regular continued fraction expansion of x is periodic. [4]
Denoting the two roots by r 1 and r 2 we distinguish three cases. If the discriminant is zero the fraction converges to the single root of multiplicity two. If the discriminant is not zero, and |r 1 | ≠ |r 2 |, the continued fraction converges to the root of maximum modulus (i.e., to the root with the greater absolute value).
The reciprocal of a proper fraction is improper, and the reciprocal of an improper fraction not equal to 1 (that is, numerator and denominator are not equal) is a proper fraction. When the numerator and denominator of a fraction are equal (for example, 7 / 7 ), its value is 1, and the fraction therefore is improper. Its reciprocal is ...
UL 310 "Standard for Electrical Quick-Connect Terminals" [4] CSA 22.2 #153, "Quick-Connect Terminals" UL 486 also specifies the testing of standard wire connectors and soldering lugs.
Four Sony CCU-D50 control units. The camera control unit (CCU) is typically part of a live television broadcast chain. It is responsible for powering the professional video camera, handling signals sent over the camera cable to and from the camera, and can be used to control various camera parameters remotely.
In mathematics, the infinite series 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1.
It is one way of expressing the composition of a mixture in a dimensionless size; mole fraction (percentage by moles, mol%) and volume fraction (percentage by volume, vol%) are others. When the prevalences of interest are those of individual chemical elements , rather than of compounds or other substances, the term mass fraction can also refer ...
For hoses and piping, a quick connect fitting, also called a push fitting, is a coupling used to provide a fast, make-or-break connection of gas or liquid transfer lines. Operated by hand, quick connect fittings replace threaded or flanged connections, which require wrenches. When equipped with self-sealing valves, quick connect fittings will ...