Problem:
Give numerical evidence to evaluate


Visualization:
Using Maple:

> f:= x -> (x^2-1)/(x^2+1);

> L:=[m, 2^m*100, f(2^m*100)];

> for m from 1 by 1 to 12 do print(evalf(L)); od;

The evidence appears to indicate that the limit is 1.