Question

For which of the values of x does limit as n approaches infinity of x^n exist?

Answer 1

There will only be a limit to x^n as n approaches infinity if x^n converges. This can only happen if \[-1\lt x \le 1\] as the values within this range decrease when x^n increases - x^n tends towards 0 as n tends towards infinity. If x = 1, x^n = 1 for any n and so the limit of x^n is 1 as n tends towards infinity. -1 is not included in the range, as x^n constantly fluctuates between -1 and 1.