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.
Prove that if converges to L and converges to M , then the series.
Given that and , find the value ofrole="math" localid="1648828282417" .
Improper Integrals: Determine whether the following improper integrals converge or diverge.
Let be a continuous, positive, and decreasing function. Complete the proof of the integral test (Theorem 7.28) by showing that if the improper integral converges, then the series localid="1649180069308" does too.
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