若72的正因數由小至大分別是a1，a2...a12，求1/a1+1/a2+.....+1/a12?
回答 (2)
2018-08-14 5:14 am
Sol
72=(2^3)*(3^2)
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(1+1/2+1/4+1/8)*(1+1/3+1/9)
=(15/8)*(13/9)
=195/72
72=(2^3)*(3^2)
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(1+1/2+1/4+1/8)*(1+1/3+1/9)
=(15/8)*(13/9)
=195/72
2018-08-13 10:01 pm
72 的公因數 有1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
1/1 +1/2 +1/3 +1/4 +1/6+1/8 + 1/9+ 1/12 +1/18/+ 1/24 +1/36+ 1/72
=(72+36+24+18+ 12+ 9+ 8+6+4+3+2+1)/72
=195/72
1/1 +1/2 +1/3 +1/4 +1/6+1/8 + 1/9+ 1/12 +1/18/+ 1/24 +1/36+ 1/72
=(72+36+24+18+ 12+ 9+ 8+6+4+3+2+1)/72
=195/72
收錄日期: 2021-04-30 22:41:43
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20180813124138AAFcUk5