Oil is being pumped from an oil field years after its opening at the rate of billion barrels per year. Example Question #10: Concepts Of Convergence And Divergence. Of a series without affecting convergence. For any, the interval for some. Which of following intervals of convergence cannot exist? The average show has a cast of 55, each earning a net average of$330 per show. Which of the following statements is true regarding the following infinite series? There are 2 series, and, and they are both convergent. By the Geometric Series Theorem, the sum of this series is given by.
The series converges. D'Angelo and West 2000, p. 259). 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? Is divergent in the question, and the constant c is 10 in this case, so is also divergent. Converges due to the comparison test. Is this profit goal realistic? We first denote the genera term of the series by: and. We know this series converges because. If it converges, what does it converge to? Determine the nature of the following series having the general term: The series is convergent. Use the contribution margin approach to compute the number of shows needed each year to earn a profit of $4, 128, 000. Therefore this series diverges. Therefore by the Limit Comparison Test.
For any such that, the interval. None of the other answers. Is convergent, divergent, or inconclusive? The field has a reserve of 16 billion barrels, and the price of oil holds steady at per barrel. Report only two categories of costs: variable and fixed. 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.
All but the highest power terms in polynomials. Notice how this series can be rewritten as. First, we reduce the series into a simpler form. Determine whether the following series converges or diverges. Is convergent by comparing the integral. Find, the amount of oil pumped from the field at time. The other variable cost is program-printing cost of $9 per guest. The limit approaches a number (converges), so the series converges. 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.
Prepare British Productions' contribution margin income statement for 155 shows performed in 2012. 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. Can usually be deleted in both numerator and denominator. To prove the series converges, the following must be true: If converges, then converges. A series is said to be convergent if it approaches some limit. Note: The starting value, in this case n=1, must be the same before adding infinite series together. Are unaffected by deleting a finite number of terms from the beginning of a series.
Other sets by this creator. The limit does not exist, so therefore the series diverges. The alternating harmonic series is a good counter example to this.
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