Which of the following statements is true regarding the following infinite series? Is the new series convergent or divergent? A series is said to be convergent if it approaches some limit. C. If the prevailing annual interest rate stays fixed at compounded continuously, what is the present value of the continuous income stream over the period of operation of the field? The series converges.
If converges, which of the following statements must be true? The series diverges, by the divergence test, because the limit of the sequence does not approach a value as. How much oil is pumped from the field during the first 3 years of operation? At some point, the terms will be less than 1, meaning when you take the third power of the term, it will be less than the original term. Which of the following statements about convergence of the series post. Annual fixed costs total$580, 500. If, then and both converge or both diverge. Is this profit goal realistic? There are 2 series, and, and they are both convergent.
First, we reduce the series into a simpler form. Compute revenue and variable costs for each show. Thus, can never be an interval of convergence. For any, the interval for some.
Is divergent in the question, and the constant c is 10 in this case, so is also divergent. Which we know is convergent. None of the other answers. We first denote the genera term of the series by: and.
Give your reasoning. Other answers are not true for a convergent series by the term test for divergence. Is convergent by comparing the integral. The limit of the term as approaches infinity is not zero. Determine the nature of the following series having the general term: The series is convergent. Therefore by the Limit Comparison Test. This is a fundamental property of series. If and are convergent series, then. By the Geometric Series Theorem, the sum of this series is given by. Use the contribution margin approach to compute the number of shows needed each year to earn a profit of $4, 128, 000. The alternating harmonic series is a good counter example to this. Cannot be an interval of convergence because a theorem states that a radius has to be either nonzero and finite, or infinite (which would imply that it has interval of convergence). Which of the following statements about convergence of the series of function. Formally, the infinite series is convergent if the sequence. The series diverges because for some and finite.
The average show sells 900 tickets at $65 per ticket. If the series formed by taking the absolute values of its terms converges (in which case it is said to be absolutely convergent), then the original series converges. The cast is paid after each show. For how many years does the field operate before it runs dry? Of a series without affecting convergence. Note: The starting value, in this case n=1, must be the same before adding infinite series together. If the series converges, then we know the terms must approach zero. Which of the following statements about convergence of the series ∑k. Other sets by this creator. Oil is being pumped from an oil field years after its opening at the rate of billion barrels per year. For some large value of,.
Since the 2 series are convergent, the sum of the convergent infinite series is also convergent. We know this series converges because. Report only two categories of costs: variable and fixed. D. If the owner of the oil field decides to sell on the first day of operation, do you think the present value determined in part (c) would be a fair asking price? If it converges, what does it converge to? To prove the series converges, the following must be true: If converges, then converges. We have and the series have the same nature. Converges due to the comparison test. We will use the Limit Comparison Test to show this result. British Productions performs London shows. None of the other answers must be true.
All but the highest power terms in polynomials. One of the following infinite series CONVERGES. The limit does not exist, so therefore the series diverges. Conversely, a series is divergent if the sequence of partial sums is divergent. There are 155 shows a year. The average show has a cast of 55, each earning a net average of$330 per show.
Infinite series can be added and subtracted with each other. Determine whether the following series converges or diverges. A convergent series need not converge to zero.
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