18. The maximum error incurred by approximating the sum of the series 1-12!sum of the first six terms is(A) 0.001190(B) 0.006944(C) 0.33333(D) 0.1250002 3 4+.3! 4! 5!(E) None of these+-by the

The given series is 1-12!+23!-34!+45!- . . . . We have to find the maximum error incurred…

Answered: The maximum error incurred by…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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11. Series k=1 For each of the following sequences {a}, decide wether the series Σak is convergent or not. You must specify what test you use, and why this test applies. (a) ak = 2, (b) a = ²+2 3k 2k +1 (c) ak = (d) ak = (e) ak = (f) ak = (g) ak = (h) ak = (i) ak = k2 (k+1)³ sin k k² (-1) In(k+2) 3k+2. cos (km)k! 10% (3k)!(k+1)! (4k)!
4. (a) How many terms of the given alternating series do we need to add in order to find the sum of the series correct to 5 decimal places? (That is, Jerror|< 0.000005.) Show your work! (b) Approximate the sum of the series correct to 5 decimal places. Show your work! 7 (-1)7+1. 2" (n!) n=1
12) There is one special “family” of series for which, if the series converges, we can determine the exact value of the series. This is the family where it really matters that we know the bounds of the summation. What family is this?
compare the series (1+x)-3=1-3x+6x2-10x3........ with ex= 1+x +x2/2 +x3/6............ Are they both convergent? How can you prove this?
1. In this problem, you'll look at the series > 1 )J: One can visualize this series as area, by drawing a k5/4 * k=10 box of area 103/4, a box of area 134 and so on. 115/4 (a) There are two ways to draw the series (as boxes) in question. Draw each of them together with the graph y= 34 on two different graphs. x5/4 (b) Use the picture to write an inequality comparing >) 1 to an improper integral. Check the k5/4 k=10 bounds of your improper integral carefully, and be sure you are comparing on the same domain. (c) Is the improper integral you wrote in (b) convergent or divergent? Explain. (d) Using the inequality you wrote in (b) and your answer to (c), what (if anything) can you conclude 1 :? about the convergence of 2 k5/4 k=10 (e) Repeat (b)-(d) with your second picture.

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The maximum error incurred by approximating the sum of the series 1- sum of the first six terms is (A) 0.001190 (B) 0.006944 (C) 0.33333 (D) 0.125000 23 + + 2! 3! 4! 5! -" by the (E) None of these