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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Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.
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.
35.
Find the values of x for which the series converges.
Given thatand, find the value ofrole="math" localid="1648828803227" .
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