Chapter 7: Q. 1TF (page 626)
Q.
A series of monomials: Find all values of \(x\) for which the series \( \sum_{k=1}^{∞} (4x)^k\) converges.
Short Answer
The value of \(x\) lies in the interval \(\left (\frac{-1}{4},\frac{1}{4} \right )\)
Chapter 7: Q. 1TF (page 626)
Q.
A series of monomials: Find all values of \(x\) for which the series \( \sum_{k=1}^{∞} (4x)^k\) converges.
The value of \(x\) lies in the interval \(\left (\frac{-1}{4},\frac{1}{4} \right )\)
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Get started for freeExplain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.
Find the values of x for which the seriesconverges.
Let 0 < p < 1. Evaluate the limit
Explain why we cannot use a p-series with 0 < p < 1 in a limit comparison test to verify the divergence of the series
Use either the divergence test or the integral test to determine whether the series in Exercises 32–43 converge or diverge. Explain why the series meets the hypotheses of the test you select.
36.
Determine whether the series converges or diverges. Give the sum of the convergent series.
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