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In this video I show that the sequence r^n is convergent and is equal to 0 when r is between 1 and -1. This is because a number whose absolute value is less than 1 becomes smaller and smaller each time it is multiplied. The negative sign only has it changing from positive to negative but the absolute value still becomes smaller. Thus the answer to the question is True. Note also when r = 1, the sequence is also convergent but it equals 1 since 1^n is always equal to 1.
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