So lim x (1-x2n)/(1+x2n) = lim x (x-2n-1)/(x-2n+1) = x * (0-1).

If | x |

So lim x (1-x 2n)/(1+x 2n) = x * (1-0)/(1+0) = x.

If |x|= 1 and x 2n =1,

So lim x (1-x2n)/(1+x2n) = x * (1-1)/(1+1) = 0.