Question: Let {xn} be a sequence. Suppose that there is an a (0, 1) such that |xn+1 - xn| < an for all nN. Prove

Let {xn} be a sequence. Suppose that there is an a āˆŠ (0, 1) such that
|xn+1 - xn| < an
for all nāˆŠN. Prove that xn ā†’ x for some x āˆŠ R.

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