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binomial expansion


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binomial coefficient

Colin Maclaurin (1698—1746) mathematician and natural philosopher

binomial theorem

 

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The application of the Maclaurin series to (1+x)n, for any value of n:, where is a binomial coefficient. The series converges and the expansion is valid in the following cases:(i) for any value of n, if −1<x<1,(ii) for any value of x, if n is a non-negative integer, in which case the series is finite, since (nr)=0 for r>n, and the expansion is that given in the binomial theorem.

(i) for any value of n, if −1<x<1,

(ii) for any value of x, if n is a non-negative integer, in which case the series is finite, since (nr)=0 for r>n, and the expansion is that given in the binomial theorem.

Subjects: Probability and Statistics.


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