4. Determine whether the following series are absolutely convergent, conditionally convergent, or diver-gent. Justify your answers.∞(a) Σ(−1)n (n − 1)n + n!nnn=1∞22n(b) Σ(-1). (Inn)n=2∞n!(0) Σ(1)" 1.3.5. (2n-1)n=3∞1(1) Σ(-1)". Innn=2

Note : '' As per guidelines we will solve first three subparts . If you want any specific subpart to…

Answered: 4. Determine whether the following…

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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D. Determine whether each of the following series are absolutely convergent, conditionally convergent, or divergent. i. Σ (-2)^² / (n + 2)! ii. Σ (-3)^/ (3n² + 6″) iii. Σ (-4)/(4"-√2n +1)
2. Determine if the series is convergent or divergent. (a) (b) (c) k=1 6.8.10. 4.7.10 k=2 8 k=1 (sin k) (k!)² (2k)! (2k + 4) (3k + 1) k³ lnk + k + 1 k5+ k³ + 1
Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges. (-1)"n' In(n + 3) 1. 2. 6 — 9п3 (n + 7)" 3. 5" (9 + n)5" (-1)"+1, (n²)4²n (n + 7)" 4. 00 5. (-6n)" 6. n2n
Evaluate the Beta function, B(2, 3).
Please help me.
A. Determine the convergent of the following series. 1 1- 2n=1 n(yn+1) 2- E1(-1)"+1! n B. Express the numbers 2.228 as a ratio of two integers.
. I II Determine whether the series is absolutely convergent, conditionally convergent, or divergent. k = 1 absolutely convergent conditionally convergent divergent
2k-1 3. Determine whether the series 2 is convergent k+4 k = 1 or divergent by the Kth - Term test ? Divergent. А. Convergent В. Conditionally connvergent С. Cannot be determined. D.
2. Which of the following series converge conditionally? E(-1)- 2+(-1)" 3+ (-1)" O 1, 1.3 1-3-5 --- (2n – 1) +(-1 3 - 5 - 7 -- (2n + 1) 1.3.5 --+ 3' 3.5 +.. 3.5-7 E(-1)" sin n+ n=1 E(-1)" In " n+1 cos (2n)! 1.3-5 ..- (2n – 1) E(-1)"ne El-1)". Vn(n+2) 1 E(-1)"n² tan n=1

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4. Determine whether the following series are absolutely convergent, conditionally convergent, or diver- gent. Justify your answers. ∞ (2) Σ(-1)" n=1 (n − 1)n + n! nn 22n (b) Σ(−1)", (Inn)n n=2 n! (c) Σ(-1)". 1.3.5... (2n-1) n=3 (d) (-1)"____