Geometric Series: Sum of x^n series = 1/(1 - x) if |x| is less than 1
In this video, I show that the infinite series xn = x0 + x1 + x2 + ... is just a geometric series, and converges if the absolute value of x is less than 1. By common convention, x0 = 1, so the first term a is 1, and the common ratio is x, thus the sum is given by the formula 1/(1 - x).
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#math #calculus #series #geometricseries #education
Timestamps
- Example 5: Find the sum of the series xn where |x| is less than 1 – 0:00
- Solution: x0 is defined as equal to 1 – 0:22
- Expanding the series yields a geometric series – 1:07
- Since the common ratio x has an absolute value less than 1, the series is convergent and equals the first term a / (1 - x) – 2:02
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