True-False Quiz Question 19: Proof that 0.99999... = 1 (Convergent Geometric Series)
In this video I show that the number 0.99999.... can be written as a convergent geometric series whose sum is equal to 1. The number 0.99999... can be written as 0.9 + 0.09 + 0.009 + ... which can further be written as 0.9 + 0.9(0.1) + 0.9(0.1)^2 + ... which is just a geometric series. In our case, r = 0.1 and is less than 1, thus the geometric series is convergent and we can apply the formula for the sum, which is just 1. Thus the answer to the question is True: 0.99999 ... = 1. Fascinating stuff!
Time stamps:
- Question 19: 0:00
- Solution: True: Geometric Series 0:14
- Sum of a Convergent Geometric Series 3:04
- Sum of Geometric Series = 1: 5:00
Full video below:
- Infinite Sequences and Series: Review and True-False Quiz:
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