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Determine whether the series is convergent or divergent. ਪੰਜਾ 1 e12

Determine whether the series is convergent or divergent. ਪੰਜਾ 1 e12

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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Question
Determine whether the series is convergent or divergent. 1 en+2 1 I en 1 The series? Justification: (If more than one test is appropriate, pick the first applicable test in the list.) OA. 00 This is a Geometric Series of the formar-¹ where a = n=1 OB. This is a Telescoping Series, lim Sn = 1 700 OC. By the Divergence Test, lim an = n->00 O D. By the Direct Comparison Test, an ≤ b O E. By the Direct Comparison Test, an ≥ b OF. By the Limit Comparison Test, let Σbn=c() where c = an lim = n∞⁰ bn ii) lim bn = 1 00 ii) f(x) dx = OI. By the Ratio Test, lim an+1 with Σ bn = Σc(), c = n 100 an OG. By the Alternating series test, i) {bn} is ultimately decreasing because the function f satisfying f(n) = bn is decreasing on the interval = T = where Σ bn = [c() where c = OJ. By the Root Test, limno |an| = OH. By the Integral Test, i) The function f satisfying f(n) = an is positive, continuous, and ultimately decreasing on the interval 5. p= and p = and its sum is and p = and (Enter "DNE" if divergent.)
Transcribed Image Text:Determine whether the series is convergent or divergent. 1 en+2 1 I en 1 The series? Justification: (If more than one test is appropriate, pick the first applicable test in the list.) OA. 00 This is a Geometric Series of the formar-¹ where a = n=1 OB. This is a Telescoping Series, lim Sn = 1 700 OC. By the Divergence Test, lim an = n->00 O D. By the Direct Comparison Test, an ≤ b O E. By the Direct Comparison Test, an ≥ b OF. By the Limit Comparison Test, let Σbn=c() where c = an lim = n∞⁰ bn ii) lim bn = 1 00 ii) f(x) dx = OI. By the Ratio Test, lim an+1 with Σ bn = Σc(), c = n 100 an OG. By the Alternating series test, i) {bn} is ultimately decreasing because the function f satisfying f(n) = bn is decreasing on the interval = T = where Σ bn = [c() where c = OJ. By the Root Test, limno |an| = OH. By the Integral Test, i) The function f satisfying f(n) = an is positive, continuous, and ultimately decreasing on the interval 5. p= and p = and its sum is and p = and (Enter "DNE" if divergent.)
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