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On a Method of obtaining De Moivre's formula in the simplest terms

Published online by Cambridge University Press:  18 August 2016

M. Charlon
M. Charlon*
Affiliation:
“Spanish Phoenix,” Madrid
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Extract

When we consider in a table of mortality the consecutive terms which express the number living at each age, we remark that the differences between those numbers are almost constant in the middle ages of life; they change afterwards, remaining however uniform for another series of terms; so that the table can be considered as a series of decreasing arithmetical progressions. Let c be the difference between lx and lx+1; and let us suppose this difference constant for n years. We shall then have for the value of the life annuity during that time.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 15 , Issue 2 , July 1869 , pp. 141 - 143
Copyright
Copyright © Institute and Faculty of Actuaries 1870

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References

* The communication of M. Pitnentel is written in French; but we have thought it more useful to give a translation. We have also altered the notation in some respects.—Ed. J. I. A.