By mathematical induction,prove that the following proposition are true for all positive integers n.
(4n+7)(5^n)-7 is divisible by 8
請詳細列式!THX A LOT!
M2 MATHS
2010-10-10 11:16 pm
回答 (1)
2010-10-10 11:31 pm
✔ 最佳答案
When n = 1 ,(4+7)(5) - 7 = 48 = 8*6 is divisible by 8 Assume when n = k the statement is true :(4k + 7)(5^k) - 7 = 8M When n = k+1 ,(4(k+1) + 7)(5^(k+1)) - 7= (4(k+1) + 7)(5^(k+1)) - [(4k + 7)(5^k) - 8M]= 5(4k + 11)(5^k) - (4k + 7)(5^k) + 8M= (5^k)(20k + 55 - 4k - 7) + 8M= (5^k)(16k + 48) + 8M= 8 [ (5^k)(2k + 6) + M ] is divisible by 8By MI it is true for any positive integers.
收錄日期: 2021-04-21 22:16:12
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20101010000051KK00785