用a(k)表示數(shù)列第k項(xiàng)
當(dāng)m=1,a(1)=1;
當(dāng)n=1;a(1+1)=λa(1)+1,即是a(2)=λ+1,
當(dāng)n=2時(shí),a(2+1)=λa(2)+2,就是a(3)=λ(λ+1)+2;
顯然對(duì)任何實(shí)數(shù)λ ,a(3)-a(2)不等于a(2)-a(1) 證畢λ為0呢如果a為等差數(shù)列,則 a(3)-a(2)=a(2)-a(1),即 λ(λ+1)+2-(λ+1)=(λ+1)-1 , 整理得:λ*λ-λ+1=0易知該方程無(wú)實(shí)數(shù)解故對(duì)任何實(shí)數(shù)λ,a都不是等差數(shù)列當(dāng)λ=0時(shí),a(3)-a(2)=1,a(2)-a(1)=0, a不是等差數(shù)列