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A sequence ₁,₂... is such that u, = -r-1 (i) (ii) n Show that Σ r=2 11+5 Hence find Σ r=8 =2_n+1 n! r-3r+1 (r-1)! convergent. r=2 - 11-00 r! and u, = in terms of n. = U₁_2 + Limit Comparison test states that for two series of the form a, and Σb, with r=k r=k r+1-² 80 a,b,≥0 for all n, if lim">0, then both Σa, and b, converges or both diverges b₁ r=k r=k when r≥ 2. -r-1 (iii) Given that ¹²- is convergent, using the test, explain why r! r=2 r-2 (r-1)! is

A sequence ₁,₂... is such that u, = -r-1 (i) (ii) n Show that Σ r=2 11+5 Hence find Σ r=8 =2_n+1 n! r-3r+1 (r-1)! convergent. r=2 - 11-00 r! and u, = in terms of n. = U₁_2 + Limit Comparison test states that for two series of the form a, and Σb, with r=k r=k r+1-² 80 a,b,≥0 for all n, if lim">0, then both Σa, and b, converges or both diverges b₁ r=k r=k when r≥ 2. -r-1 (iii) Given that ¹²- is convergent, using the test, explain why r! r=2 r-2 (r-1)! is

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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1 A sequence u,₁,U₂... is such that u, = r! (i) (ii) Show that n r=2 11+5 Hence find Σ (iii) Given that convergent. r² -r-1 r! r=2 r²-3r+1 = 2 8(r-1)! ²- n+1 n! r! and u = U_2 + r-2 Limit Comparison test states that for two series of the form a, and b, with r=k r=k in terms of n. a₁ a,b 20 for all n, if lim- ->0, then both Σa, and b, converges or both diverges 11-8 b. 11 r=k r=k r+1-r² r! 11 when /> 2. -1 is convergent, using the test, explain why r-2 (r-1)! is
Transcribed Image Text:1 A sequence u,₁,U₂... is such that u, = r! (i) (ii) Show that n r=2 11+5 Hence find Σ (iii) Given that convergent. r² -r-1 r! r=2 r²-3r+1 = 2 8(r-1)! ²- n+1 n! r! and u = U_2 + r-2 Limit Comparison test states that for two series of the form a, and b, with r=k r=k in terms of n. a₁ a,b 20 for all n, if lim- ->0, then both Σa, and b, converges or both diverges 11-8 b. 11 r=k r=k r+1-r² r! 11 when /> 2. -1 is convergent, using the test, explain why r-2 (r-1)! is
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