Binomial theorem Questions and Solution - Binomial Theorem and Negative Exponents The Binomial Theorem already mention only deals with finite expansion

Binomial theorem Questions and Solution - Binomial Theorem...

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Binomial Theorem and Negative Exponents The Binomial Theorem already mention only deals with finite expansion. If for instance we wished to use negative or fractional exponents then it would not be possible to expand. Also the n c r button can only be used for positive integers. Around 1665 Newton generalised the formula to allow the use of negative and fractional exponents. Newton's generalised Binomial Theorem allows us to expand binomial expressions for any rational value of n . For example ( x + y ) -2 . A rational value of n is a number which can be expressed as a ratio of two integers. This now meant that you could create an infinite series. This binomial series is valid for any real number n if | x | < 1. For example: If n is not a positive integer, the expansion would be infinite and an approximation would be created. The approximation is only valid if the sequence converges, this only happens if x is small enough. For larger values of x, the sequence will diverge.
Negative Exponentials worksheet

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