MI MATH F.4
2009-11-08 8:33 pm
Let a=2 and ak=a(k-1)+4 for all integers k大過or=2 prove by mathematical induction that an=4n-2 for all positive integers n
回答 (1)
2009-11-08 8:39 pm
✔ 最佳答案
Let P(n) be the statement " a_n=4n-2 " for all positive integers nWhen n=1,a_1=2=4*1-2. LHS=RHS. So P(1) is true
Assume that P(k) is true. i.e. a_k=4k-2
When n=k+1, a_k+1=a_k+4=4k-2+4=4k+2=4(k+1)-2
LHS=RHS. So P(k+1) is true
By M.I. for all positive integers n, P(n) is true.
收錄日期: 2021-04-26 13:59:48
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091108000051KK00615