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Prove that, for x ∈ C, when |x| < 1, lim_n→∞ |x_n| = 0. Note: To...

Prove that, for x ∈ C, when |x| < 1, lim_n→∞ |x_n| = 0.

Note:

To prove this, show that an = xn is monotone decreasing and bounded from below. Apply the Monotone sequence theorem. Then, use the algebra of limits, say limn→∞ |xn| = A, to prove that A = 0.

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