定义:a是不为1的有理数,我们把1/1-a称为a的差倒数.如:2的差倒数是1/1-2=-1,-1的差倒数是
问题描述:
定义:a是不为1的有理数,我们把1/1-a称为a的差倒数.如:2的差倒数是1/1-2=-1,-1的差倒数是
1/1-(-1)=1/2,已知a1=1/2.a2是a1的差倒数,则a2=( ),a3是a2的差倒数,则a3=( ),a4是a3的差倒数,则a4=( ),以此类推,则a2010=( )
答
a2 = 1/(1-1/2) = 1/(1/2) = 2
a3 = 1/(1-2) = 1/(-1) = -1
a4 = 1/(1-(-1)) = 1/2 = a1
a2010 = a(3+2007) = a(3+3*669) = a3 = -1