Binomial Theorem and Negative Exponentials

(1+x)-1

What is a Negative Exponential?

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 ncr button can only be used for

positive integers.

Problems using Binomial Theorem and Negative or Fractional Exponents

(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 Influences

Newton’s Binomial Theorem allows us to expand binomial expressions for any rational valued exponent.

How it works

What is a Rational Number???

1/2A rational number is a number which

can be expressed as a ratio of two integers

√3

Newton’s Binomial Theorem