# Page:Harvard Law Review Volume 1.djvu/345

be £1,200, the second £720, the third £432, etc. In this case it soon becomes evident that the securities will never be exhausted, though the above process be carried on ad infinitum. Now the aggregate of all the dividends may be readily determined as follows: The numbers 1,200, 720, 432, etc., will be found to constitute a geometrical progression, the ratio (${\displaystyle e}$) of the terms of which is ₁₂₀₀ ⁷²⁰––– = ⅗, and their number infinity. Taking the formula ${\displaystyle s={\begin{matrix}{\frac {a}{1-e}}\end{matrix}}}$ (${\displaystyle a}$ being the first term of the progression) we find the sum of the dividends in this case to be £3,000. The total amount of the securities to be divided among all the other creditors will be found to equal £1,200, or the first dividend. For if the bill-holders’ dividends are ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$, ${\displaystyle d}$, etc., to infinity, those of the general creditors will be ${\displaystyle a-b}$, ${\displaystyle b-c}$, ${\displaystyle c-d}$, etc.; the last dividend being infinitely small, it will be found on addition that all the terms except ${\displaystyle a}$ vanish. Having thus ascertained the total amount due the general creditors, it will only remain to distribute it in proportion to their respective claims.