(1+x) -1

The binomial theorem already mentioned only deals with Finite expansion. If for instance we wished to use Negative or Fractional exponents it would not be possible to expand. Also the n c r button can only be used for positive integers. (1+x) -1.5 =???

At around 1665 Newton generalised the formula to allow the use of negative and fractional exponents. Newton’s first results concerning Binomial Series were given by Sir Isaac Newton in the study of areas enclosed under a curve. The Binomial series is sometimes referred to Newton’s Binomial Theorem. Newton gives no proof and is not explicit about the nature of the series.

Newton’s Binomial Theorem allows us to expand binomial expressions for any rational valued exponent. What is a Rational Number??? 1/2 A rational number is a number which can be expressed as a ratio of two integers √3