Sentence Examples

  • Consideration of the binomial theorem for fractional index, or of the continued fraction representing a surd, or of theorems such as Wallis's theorem (� 64), shows that a sequence, every term of which is rational, may have as its limit an irrational number, i.e.
  • (iv.) The procedure is sometimes stated differently, the transposition being regarded as a corollary from a general theorem that the roots of an equation are not altered if the same expression is added to or subtracted from both members of the equation.
  • � 21 (ii.)) is that we do not need the general theorem, and that it is unwise to cultivate the habit of laying down a general law as a justification for an isolated action.
  • The binomial theorem gives a formula for writing down the coefficient of any stated term in the expansion of any stated power of a given binomial.
  • (ii.) We can prove the theorem of � 41 (v.) by a double application of the method.

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