The limit does not exist, so therefore the series diverges. Is the new series convergent or divergent? Students also viewed. British Productions performs London shows. Explain your reasoning. Example Question #10: Concepts Of Convergence And Divergence. D'Angelo and West 2000, p. 259). The series diverges, by the divergence test, because the limit of the sequence does not approach a value as. Which of the following statements is true regarding the following infinite series? The divergence tests states for a series, if is either nonzero or does not exist, then the series diverges.
Which of following intervals of convergence cannot exist? Find, the amount of oil pumped from the field at time. Notice how this series can be rewritten as. Conversely, a series is divergent if the sequence of partial sums is divergent. This is a fundamental property of series. 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? If, then and both converge or both diverge. Use the contribution margin approach to compute the number of shows needed each year to earn a profit of $4, 128, 000. Is convergent, divergent, or inconclusive? 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. If and are convergent series, then. The series diverges because for some and finite.
Thus, can never be an interval of convergence. One of the following infinite series CONVERGES. The series converges. Determine the nature of the following series having the general term: The series is convergent.
None of the other answers must be true. Annual fixed costs total$580, 500. The limit of the term as approaches infinity is not zero. Is divergent in the question, and the constant c is 10 in this case, so is also divergent.
There are 155 shows a year. All Calculus 2 Resources. For any such that, the interval.
Converges due to the comparison test. We will use the Limit Comparison Test to show this result. We have and the series have the same nature. Other answers are not true for a convergent series by the term test for divergence.
The alternating harmonic series is a good counter example to this. Give your reasoning. Determine whether the following series converges or diverges. Formally, the infinite series is convergent if the sequence. A series is said to be convergent if it approaches some limit. Compute revenue and variable costs for each show. There are 2 series, and, and they are both convergent. Prepare British Productions' contribution margin income statement for 155 shows performed in 2012.
Other sets by this creator. For how many years does the field operate before it runs dry? For any constant c, if is convergent then is convergent, and if is divergent, is divergent. You have a divergent series, and you multiply it by a constant 10. Can usually be deleted in both numerator and denominator. Are unaffected by deleting a finite number of terms from the beginning of a series.
Which we know is convergent.
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