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For the series below calculate find the number of terms n that must be added in...
Does the following series converge absolutely, converge conditionally or diverge? jo (-1)4+1 27k diverges converges absolutely converges conditionally Box 1: Select the best answer For the series below calculate find the number of terms n that must be added in order to find the sum to the indicated accuracy. 2 (-1)"+1) 2n3 +4 error] < 0.01 n= Preview Find the sum of the series correct to 2 decimal places. Sum = Preview Box 1: Enter your answer as a number...
How many terms of the series do we need to add in order to find the sum to the indicated accuracy? ËS-15-, ulerorl 5 0.001 ; (error] < 0.0001. ng n=1 Answer: Note: Enter the smallest possible integer. o find the sum to the indicated accuracy? È (-1)- Jerror] < 0.0008. error < 0.0008. ) 2
(1 point) What is the least number of terms of the series that we need to add in order to approximate the sum to within 0,003 of the actual sum of the series? (-1)"-1 n2 n 1 ISum - Sk Slak+1|| Recall that for an alternating series: error number of terms: N (Don't forget to enter the smallest possible integer.) approximation of sum: S (1 point) What is the least number of terms of the series that we need to...
I'm having difficulty how many terms need to be added in. Test the series for convergence or divergence. 00 Σ (-1)" n2n n = 1 Identify bn. 1 n2" Evaluate the following limit. lim bn n → 00 0 Since lim bn O and bn + 1 s bn for all n, the series is convergent n00 If the series is convergent, use the Alternating Series Estimation Theorem to determine how many terms we need to add in order to...
write a recursive algorithm to find the sum of the first N terms of the series 1, 1/2, 1/3, ... 1/N
a,b,c and d (-1) 4. (3 points each) Consider the series n° +2n +3 (a) Prove that this series converges absolutely. (b) Show that this series satisfies all three conditions of the Alternating Series Test. HI11-2212, JL ILG-2020 Test #3 (c) What value of n guarantees that the partial sum 8, approximates the sum of this series to within an accuracy of 0.01? (d) Find the sum of the series with this accuracy (by finding the appropriate partial sum sn,...
4.3 Devilish Series The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may dr is why these series have produced so dany fallacies and so many paradoxes. Neils Henrik Abel (Norwegian Mathematician; 1802 - 1829) There is no reason that infinite series must have all positive terms. For example, the alter- nating harmonic series is built from the harmonic series but with every other...
QUESTION 1 10 po Verify in your own mind that you can use the Alternating Series Test to show that the following series is convergent. How many terms of the series do we need to add in order to find the sum to the accuracy error < 0.00005? (-1)"+1 n=1 n6 Enter your answer as a whole number.
Consider the following alternating series. (-1)*+ 1 3k k=1 (a) Show that the series satisfies the conditions of the Alternating Series Test. 1 3" Since lim o and an + 1 for all n, the series is convergent (b) How many terms must be added so the error in using the sum S, of the first n terms as an approximation to the sum n=10 X (c) Approximate the sum of the series so that the error is less than...
(2) Show that the series converges. Determine the smallest number of terms required to ap- proximate the sum of the series with e < 10-3. (-1)" tin (b) --- n=z In(n2) n= 1