The series converges. Is convergent by comparing the integral. Find, the amount of oil pumped from the field at time. For any such that, the interval. The limit does not exist, so therefore the series diverges. Infinite series can be added and subtracted with each other. For how many years does the field operate before it runs dry? Is this profit goal realistic? Thus, can never be an interval of convergence. For any, the interval for some. If it converges, what does it converge to? Which of the following statements is true regarding the following infinite series?
Explain your reasoning. 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. A series is said to be convergent if it approaches some limit. A convergent series need not converge to zero. Therefore this series diverges. The field has a reserve of 16 billion barrels, and the price of oil holds steady at per barrel. The alternating harmonic series is a good counter example to this. We first denote the genera term of the series by: and. Students also viewed. If converges, which of the following statements must be true? None of the other answers. 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.
Conversely, a series is divergent if the sequence of partial sums is divergent. The series diverges, by the divergence test, because the limit of the sequence does not approach a value as. For any constant c, if is convergent then is convergent, and if is divergent, is divergent. The series diverges because for some and finite. 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). To prove the series converges, the following must be true: If converges, then converges. The cast is paid after each show. Therefore by the Limit Comparison Test. 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? Example Question #10: Concepts Of Convergence And Divergence. In addition, the limit of the partial sums refers to the value the series converges to.
Are unaffected by deleting a finite number of terms from the beginning of a series. Annual fixed costs total$580, 500. Determine the nature of the following series having the general term: The series is convergent. If the series converges, then we know the terms must approach zero. We will use the Limit Comparison Test to show this result. Since the 2 series are convergent, the sum of the convergent infinite series is also convergent. For some large value of,. First, we reduce the series into a simpler form. Is convergent, divergent, or inconclusive? Converges due to the comparison test. Other sets by this creator.
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. Compute revenue and variable costs for each show. We have and the series have the same nature. The other variable cost is program-printing cost of $9 per guest.
Notice how this series can be rewritten as. The limit approaches a number (converges), so the series converges. Other answers are not true for a convergent series by the term test for divergence. All but the highest power terms in polynomials. Give your reasoning.
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