Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.

jsMath
發新話題
打印

費式數列的數學歸納法證明

費式數列的數學歸納法證明

Consider the recurrence relation for Fibonacci numbers F(n)=F(n1)+F(n2). Without solving this recurrence, compare F(n) to G(n) defined by the recurrence G(n)=G(n1)+G(n2)+1. It seems obvious that G(n)F(n)(because of the extra 1). Yet the following is a seemingly valid proof(by induction) that G(n)=F(n)1. We assume, by induction, that G(k)=F(k)1 for all k such that 1kn, and we consider G(n+1):
G(n+1)=G(n)+G(n1)+1=F(n)1+F(n1)1+1=F(n+1)1
What is wrong with this proof?
請各位老師幫忙  謝謝
(看不出哪裡有錯誤)

TOP

回復 1# P78961118 的帖子

上面的數學歸納法漏掉了檢查初始值的步驟。

而且 G(n) 數列的遞迴定義式也沒有定義初始條件。

多喝水。

TOP

發新話題