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Will H
Lv 7
Determine the interval of convergence of the power series?
Determine the interval of convergence of the power series
∞
Σ (1/(3^(n)*n)) * (x - 1)^n
n=1
2 Answers
Relevance
- 10 years agoFavourite answer
Ratio test:
lim{n→∞} (x - 1)^(n + 1) / (x - 1)^n * 3^n / 3^(n + 1) * n / (n + 1)
|(x - 1) * 1/3 * 1| < 1
|x - 1| < 3
-3 < x - 1 < 3
-2 < x < 4
Test the endpoints, which simplify the series down to (-1)^n / n and 1/n. The alternating harmonic converges (x = -2) but the regular harmonic doesn't.
-2 <= x < 4.
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