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(2n + 1)x Please explan thisn Determine whether the series 2 sin- converges or diverg as. If it converges, find its sum. n=0 (4r+1)x 31 and Land howit nelates to the Since sin 1 and sin =-1 and the angle may be incrementec by any multiple of 2x, then sin (4r+3)x sin =-1, (any r). tow does this nelate to the ansuer? Examine the partial sums of the series. The expanded series is sin + sin+ sin 5x + sin,+ sin +.... 2 ansue 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 e = sin (8+2mx), all the even terms are equal to 1, and al the odd terms are equal to -1. Evaluating each term, the series is 1+(-1)+1+(-1)+1+. The partial sums altemate between 1 and 0, tending to (2n+ 1)x neither value. Therefore, lim E sin- k00 n=0 does not exist and the series diverges.

(2n + 1)x Please explan thisn Determine whether the series 2 sin- converges or diverg as. If it converges, find its sum. n=0 (4r+1)x 31 and Land howit nelates to the Since sin 1 and sin =-1 and the angle may be incrementec by any multiple of 2x, then sin (4r+3)x sin =-1, (any r). tow does this nelate to the ansuer? Examine the partial sums of the series. The expanded series is sin + sin+ sin 5x + sin,+ sin +.... 2 ansue 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 e = sin (8+2mx), all the even terms are equal to 1, and al the odd terms are equal to -1. Evaluating each term, the series is 1+(-1)+1+(-1)+1+. The partial sums altemate between 1 and 0, tending to (2n+ 1)x neither value. Therefore, lim E sin- k00 n=0 does not exist and the series diverges.

Advanced Engineering Mathematics
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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(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.
Transcribed Image Text:(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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