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Which of the sequences in Exercises 125–134 converge, and which diverge? Give reasons for your answers. 125. a, = 1 1 126. а, — п п п 2" - 1 2" – 1 127. a, = 2" 128. ат 3" п +1 129. a, = ((-1)" + 1) п 130. The first term of a sequence is x1 = cos (1). The next terms are x2 = x1 or cos (2), whichever is larger; and x3 = x or cos (3), whichever is larger (farther to the right). In general, %3D Xn+1 = max {Xn, cos (n + 1)}. 1 + V2n Vn n + 1 131. a, = 132. an п 4"+1 + 3" 133. an = 134. ај — 1, а,+1 — 2а, — 3 4" ||

Which of the sequences in Exercises 125–134 converge, and which diverge? Give reasons for your answers. 125. a, = 1 1 126. а, — п п п 2" - 1 2" – 1 127. a, = 2" 128. ат 3" п +1 129. a, = ((-1)" + 1) п 130. The first term of a sequence is x1 = cos (1). The next terms are x2 = x1 or cos (2), whichever is larger; and x3 = x or cos (3), whichever is larger (farther to the right). In general, %3D Xn+1 = max {Xn, cos (n + 1)}. 1 + V2n Vn n + 1 131. a, = 132. an п 4"+1 + 3" 133. an = 134. ај — 1, а,+1 — 2а, — 3 4" ||

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 1E
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Which of the sequences in Exercises 125–134 converge, and which diverge? Give reasons for your answers. 125. a, = 1 1 126. а, — п п п 2" - 1 2" – 1 127. a, = 2" 128. ат 3" п +1 129. a, = ((-1)" + 1) п 130. The first term of a sequence is x1 = cos (1). The next terms are x2 = x1 or cos (2), whichever is larger; and x3 = x or cos (3), whichever is larger (farther to the right). In general, %3D Xn+1 = max {Xn, cos (n + 1)}. 1 + V2n Vn n + 1 131. a, = 132. an п 4"+1 + 3" 133. an = 134. ај — 1, а,+1 — 2а, — 3 4" ||
Transcribed Image Text:Which of the sequences in Exercises 125–134 converge, and which diverge? Give reasons for your answers. 125. a, = 1 1 126. а, — п п п 2" - 1 2" – 1 127. a, = 2" 128. ат 3" п +1 129. a, = ((-1)" + 1) п 130. The first term of a sequence is x1 = cos (1). The next terms are x2 = x1 or cos (2), whichever is larger; and x3 = x or cos (3), whichever is larger (farther to the right). In general, %3D Xn+1 = max {Xn, cos (n + 1)}. 1 + V2n Vn n + 1 131. a, = 132. an п 4"+1 + 3" 133. an = 134. ај — 1, а,+1 — 2а, — 3 4" ||
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