If you finish all of the above Successful completion of the following will add up to 2 additional...
6. For each given series, complete the following tasks: (i) Prove that the series converges ab- solutely; (i) Show that the series satisfies all conditions of the Alternating Series Test; (ii) Find the partial sum sy of the series, and then estimate its remainder Ra: (iv) Determine how many terms are needed to approximate the sum of the series accurate to within 0.001, and then find this approximation. (a) L (b) Σ 27! 6. For each given series, complete the...
To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 also investigate convergence using other methods.) Find the value of e-24 dx = Preview Ji What does this value tell you about the convergence of the series e-2n? the series definitely diverges the series might converge or diverge: we need more information the series definitely converges Compute the value of the following improper integral, if it...
Let Pbé à pósitive, continuous, and decreasing function for x 2 1, such that an-n). If the series an n 1 converges to S, then the remainder RN -S-Sw is bounded by Use the result above to approximate the sum of the convergent series using the indicated number of terms. (Round your answers to four decimal place Σ ,T, ten terms n2 +1' Include an estimate of the maximum error for your approximation. (Give your answer to four decimal places.)...
1. 2. (1 point) Consider the following convergent series: Suppose that you want to approximate the value of this series by computing a partial sum, then bounding the error using the integral remainder estimate. In order to bound the value of the series between two numbers which are no more than 10 apart, what is the fewest number of terms of the series you would need? Fewest number of terms is 585 (1 point) Consider the following series: le(n Use...
all but dont work on the julia box one which is 2 i think so 1-3-4 Fitchburg State University Department of Mathematics Project #3 Math 2400: Calculus II April 11, 2019 project for Calculus II. You may work on this with up to one other fellow student. Answer all questions completely and type or neatly write out. The final project should be turned in by Tueeday, April 23. How is it that we generate For this project it helps to...