證明１８｜２２ｎ＋２４ｎ－１０。(ｎ＝任意自然數)
2007-11-10 07:21:56 · 3 個解答 · 發問者 ? 4 in 科學 ➔ 數學
1. n=1, ２^２ｎ＋２４ｎ－１０=4+24-10=18為18的倍數
2.令 ２^２k＋２４k－１０=18a (a為自然數),
２^２(k+1)＋２４(k+1)－１０=4*２^２k＋２４k+１4
=4(２^２k＋２４k－１０)-72k+54=4*18a-18(4k-3)=18(4a-4k+3)
為18的倍數, 由數學歸納法得證.
2007-11-10 08:26:58 · answer #1 · answered by GONG 6 · 0⤊ 0⤋
不就是數學歸納法嗎= =?
2007-11-10 12:29:26 · answer #2 · answered by Anonymous · 0⤊ 0⤋
ＴＯ：GONG
如何知道２^２k＋２４k－１０=18a ???
2007-11-10 10:36:10 · answer #3 · answered by 3M 6 · 0⤊ 0⤋