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On the Summation of a Compound Series, and its application to a Problem in Probabilities

Published online by Cambridge University Press:  18 August 2016

Bishop Terrot
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Extract

The series proposed for solution in the following paper is—

The law of this series is manifest. Each term is the product of two factorials—the first consisting of p, and the latter of q, factors; and in each successive term, the factors of the first factorial are each diminished by one. and those of the latter increased by one.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 5 , Issue 1 , 1855 , pp. 1 - 6
Copyright
Copyright © Institute and Faculty of Actuaries 1855

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References

* The coefficient (U of Galloway's Treatise), expressing the number of different ways in which p white and q black balls can be combined in p+q trials, is here omitted. This is immaterial, as it disappears in the expression