True-False Quiz Question 11: Convergent Sequence r^n when |r| is less than 1

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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.

Time stamps:

• Question 11: 0:00
• Solution: 0:14
• Visual illustration: 1:17
  • Visualization of powers of negative r: 2:34

Full video below:

• Infinite Sequences and Series: Review and True-False Quiz:

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