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 freeIn Exercises 48–51 find all values of p so that the series converges.
Use either the divergence test or the integral test to determine whether the series in Given Exercises converge or diverge. Explain why the series meets the hypotheses of the test you select.
Whenever a certain ball is dropped, it always rebounds to a height60% of its original position. What is the total distance the ball travels before coming to rest when it is dropped from a height of 1 meter?
Explain 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.
Express each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.
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