→ stupidkai :感謝你 03/18 14:01
※ 引述《stupidkai (stupid nomore!)》之銘言：
: 1
: ----------------------------- 的整數部分為多少？
: 1 1 1 1
: --- + --- + --- + ... + ---
: 890 891 892 899
: 算好久都算不出來，請高手幫忙，感激不盡
可先觀察分母。頭尾兩個兩個一組，共五組
a = 1/890 +1/899 = 1789/890*899
b = 1/891 +1/898 = 1789/891*898
c = 1/892 +1/897 = 1789/892*897
d = 1/893 +1/896 = 1789/893*896
e = 1/894 +1/895 = 1789/894*895
知 a > b > c > d > e
=> 5a > (a+b+c+d+e) > 5e
=> 89.447 約 = 1/5a < 1/(a+b+c+d+e) < 1/5e 約 = 89.4499
所以整數部分為 89 #
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