Fast pls solve this question correctly in 5 min pls I will give u like for sure Sub 52.(a) Let the series an bedefined by a₁ = 1 andan+13+ sin n√n18n=1Use the Ratio Test to determine ifΣn-1 an converges or diverges.(b) Use the Ratio Test to determine if250enanconverges or diverges.if n ≥ 1

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Answered: 52.(a) Let the series an be defined by…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 5RE

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Solve for x: z=x.
(b) Let's rearrange the alternating harmonic series: i. We have = In 2. %3D 3 4. 10 Now group together the terms as follows: 3 10 12 We can write this as a series D' Determine A,B, C, and D. (Think about even and odd numbers.) ii. Explain why this is a rearrangement of the alternating harmonic series. In other words, show that every term from the alternating harmonic series appears somewhere in this new 4- (β-#) & rearrangement. iii. Now do the subtraction that you have in the parenthesis (-) and factor out . Explain how this shows that In 2. .... 3 10 12
(2n+ 1)x Please explan Determine whether the series sin- converges or diverg es. If it converges, find its sum. thish L and how it nelotes to the n-D0 (4r + 1)x Since sin =1 and sin =-1 and the angle may be incremente by any multiple of 2x, then sin 2 =1 and (4r+3)a sin =-1, (any r). How does this nelate to the answer. Examine the partial sums of the series. The expanded series is sin 3n 5x + sin + sin ,+ sin + sin+ .. ansver Notice that the angles in consecutive even terms (n is even) differ by 2x, and the angles in consecutive odd terms (n is odd) differ by 2x. Since sin 0 = sin (0+2mx), all the even terms are equal to 1, and all the odd terms are equal to -1. Evaluating each term, the series is 1+(-1)+1+(-1)+1+ The partial sums altermate between 1 and 0, tending to (2n + 1)a neither value. Therefore, lim sin- k00 n=0 does not exist and the series diverges. detail. Pelease explain n thanke gou.
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4) Rewrite as a power series in the form E an x" : n=0 x7 f(x) = 4 + x?
please help me with that
What is the exact value of the series from k=2 to 100 of (2/(k-1))-(2/(k+1))?

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52.(a) Let the series an be defined by a₁ = 1 and an+1 3 + sin n √n 18 n=1 Use the Ratio Test to determine if Σn-1 an converges or diverges. (b) Use the Ratio Test to determine if n 50 en an if n ≥ 1 converges or diverges.