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一個規律數列是否碰整數數學問題
Aug 21st 2013, 05:22

(1) 分子: 10,17,26,37,50,....

第1級差: 7,9,11,13,.....

第2級差: 2,2,2,...

第2級公式:

an=a+(n-1)d1+(n-1)(n-2)d2/2

=10+(n-1)7+(n-1)(n-2)2/2

=10+(n-1)(7+n-2)

=10+(n-1)(n+5)

=n^2+4n+5

(2) 分母: 3,5,7,9,11,.....

bn=2n+1

(3) 合併

cn=an/bn=(n^2+4n+5)/(2n+1)

c6=(36+24+5)/13=65/13=5........ans

第6項剛好整數=5


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