The other variable cost is program-printing cost of $9 per guest. Which of the following statements is true regarding the following infinite series? This is a fundamental property of series. Explain your reasoning. Which of the following statements about convergence of the series here. Can usually be deleted in both numerator and denominator. None of the other answers must be true. Other answers are not true for a convergent series by the term test for divergence. There are 155 shows a year.
The series converges. For any constant c, if is convergent then is convergent, and if is divergent, is divergent. Which of following intervals of convergence cannot exist? The series diverges, by the divergence test, because the limit of the sequence does not approach a value as. Infinite series can be added and subtracted with each other. You have a divergent series, and you multiply it by a constant 10. For how many years does the field operate before it runs dry? Concepts of Convergence and Divergence - Calculus 2. Which we know is convergent. We have and the series have the same nature. The series diverges because for some and finite.
A series is said to be convergent if it approaches some limit. 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). Find, the amount of oil pumped from the field at time.
Use the contribution margin approach to compute the number of shows needed each year to earn a profit of $4, 128, 000. We will use the Limit Comparison Test to show this result. 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? 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. The field has a reserve of 16 billion barrels, and the price of oil holds steady at per barrel. Which of the following statements about convergence of the series circuit. A convergent series need not converge to zero. Are unaffected by deleting a finite number of terms from the beginning of a series. For some large value of,.
The divergence tests states for a series, if is either nonzero or does not exist, then the series diverges. Therefore this series diverges. For any, the interval for some. Formally, the infinite series is convergent if the sequence.
The alternating harmonic series is a good counter example to this. Convergence and divergence. The limit approaches a number (converges), so the series converges. Is divergent in the question, and the constant c is 10 in this case, so is also divergent. D'Angelo and West 2000, p. 259). Since for all values of k, we can multiply both side of the equation by the inequality and get for all values of k. Since is a convergent p-series with, hence also converges by the comparison test. Determine whether the following series converges or diverges. If and are convergent series, then.
All but the highest power terms in polynomials. British Productions performs London shows. There are 2 series, and, and they are both convergent. One of the following infinite series CONVERGES. We first denote the genera term of the series by: and. We know this series converges because. Prepare British Productions' contribution margin income statement for 155 shows performed in 2012. Students also viewed. Since the 2 series are convergent, the sum of the convergent infinite series is also convergent. The average show has a cast of 55, each earning a net average of$330 per show. Now, we simply evaluate the limit: The shortcut that was used to evaluate the limit as n approaches infinity was that the coefficients of the highest powered term in numerator and denominator were divided.
Thus, can never be an interval of convergence. The average show sells 900 tickets at $65 per ticket. If it converges, what does it converge to? Note: The starting value, in this case n=1, must be the same before adding infinite series together.
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?
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