If converges, which of the following statements must be true? 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. There are 155 shows a year. If and are convergent series, then. 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. In addition, the limit of the partial sums refers to the value the series converges to. We will use the Limit Comparison Test to show this result. Is convergent, divergent, or inconclusive? The field has a reserve of 16 billion barrels, and the price of oil holds steady at per barrel. Is convergent by comparing the integral. The divergence tests states for a series, if is either nonzero or does not exist, then the series diverges. Therefore this series diverges.
Prepare British Productions' contribution margin income statement for 155 shows performed in 2012. Which of following intervals of convergence cannot exist? The cast is paid after each show. Conversely, a series is divergent if the sequence of partial sums is divergent.
We start with the equation. The limit does not exist, so therefore the series diverges. 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 we know is convergent. Other answers are not true for a convergent series by the term test for divergence. None of the other answers must be true.
Converges due to the comparison test. Therefore by the Limit Comparison Test. Are unaffected by deleting a finite number of terms from the beginning of a series. The other variable cost is program-printing cost of $9 per guest. D'Angelo and West 2000, p. 259). No additional shows can be held as the theater is also used by other production companies. The limit of the term as approaches infinity is not zero. Other sets by this creator. Convergence and divergence.
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 average show has a cast of 55, each earning a net average of$330 per show. If it converges, what does it converge to? All Calculus 2 Resources.
First, we reduce the series into a simpler form. For how many years does the field operate before it runs dry? Determine whether the following series converges or diverges: The series conditionally converges. Of a series without affecting convergence. For any such that, the interval. Use the contribution margin approach to compute the number of shows needed each year to earn a profit of $4, 128, 000. Annual fixed costs total$580, 500. Report only two categories of costs: variable and fixed.
Thus, can never be an interval of convergence. Is this profit goal realistic? Use the income statement equation approach to compute the number of shows British Productions must perform each year to break even. How much oil is pumped from the field during the first 3 years of operation? Note: The starting value, in this case n=1, must be the same before adding infinite series together. Since the 2 series are convergent, the sum of the convergent infinite series is also convergent. This is a fundamental property of series. Give your reasoning.
By the Geometric Series Theorem, the sum of this series is given by. The alternating harmonic series is a good counter example to this. You have a divergent series, and you multiply it by a constant 10. Formally, the infinite series is convergent if the sequence. There are 2 series, and, and they are both convergent. A series is said to be convergent if it approaches some limit. Students also viewed. Oil is being pumped from an oil field years after its opening at the rate of billion barrels per year. Can usually be deleted in both numerator and denominator.
We have and the series have the same nature. If the series converges, then we know the terms must approach zero. One of the following infinite series CONVERGES. A convergent series need not converge to zero. Is divergent in the question, and the constant c is 10 in this case, so is also divergent. Compute revenue and variable costs for each show. British Productions performs London shows.
The limit approaches a number (converges), so the series converges. Infinite series can be added and subtracted with each other. If, then and both converge or both diverge.
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