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Chinese Foundation of Japanese Math
Plate 2.5. How many barrels are in the stack? From the Jinko¯ - ki, c. 1818. (Collection of Fukagawa Hidetoshi.)
(2) A boy saves money in the following way: On day one he saves 1 mon, on day two he saves 2 mon, and on day three he saves 22 = 4 mon. How much money in total will he have saved after 30 days? The answer to (1) can be found on page 56.
Answer 2: The boy’s total savings amounts to a geometric series of the form n
S = a + ar + ar 2 + . . . + ar n = a
∑r k =0
It is well known that such a series sums to S = a(1 – r n + 1)/(1 - r).
k.