Question

已知a1= -(1/3),a2是a1的差倒数,a3是a2的差倒数,a4是a3的差倒数,……,以此推类,a2012=

Answer 1

a2=1/(1-a1)=3/4,a3=1/(1-a2)=4,a4=1/(1-a3)=-1/3=a1,

so,n=1,4,7,10...时,an=a1,

显然,n=1+3k,k属于自然数

2012=(1+3*670)+1

即a2011=a1,有a2012=a2=3/4