(a) Prove the convergence or divergence of each of the following series: 1! 2! 3! (i) + + 22 +1 + + n! 2n + 1 +... 2+1 2³ +1 1 (ii) -1)n-1 +... 1- 5 1 3 + 2n 1

Q: For which series monotone and bounded sequences theorem can be applied for the convergency? 2" a, =…

A: We have to find which series monotone and bounded sequence theorem can be applied for convergence.

Q: Determine whether each of the following series are absolutely convergent, conditionally convergent,…

A: As per the question we are given the following three infinite series : ∑ (-2)n² / (n + 2)! ∑ (-3)n…

Q: (a) Use the binomial series to expand 00 3. 5:7. •(2n + 1) 5 + 5 ) x2n 2n. n! n = 1 1· 3· 5. *·(2n –…

A: Here by using the binomial series we have to expand  5/√(1-x2) .

Q: For which series monotone and bounded sequences theorem can be opplied for the convergency 2" a,…

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Q: Determine by ratio test the convergence or divergence of the series 1 19 2! 19 3! 3 4! 19 4 () 19 1+…

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Q: 3. Determine which of the following series converge: (a) ( d) Σ 50 + 2n n= n=1 n O n (e) n=1 (2n2 –…

A: Please note that according to guidelines only first 3subparts is solved.

Q: Show that the following series are convergent and find their sums: a) 1ײ×3 +2×3×4 +...+ n(n+1)(n+2)…

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Q: Determine whether the series is (are) converge(s) absolutely. 3* -1 A and D C and D None A and C

A: Solution is given as below:

Q: . Determine if the following series is convergent or divergent (−1)n+1n² n³+4 b) Σ=1 Σn=1 700 a)…

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Q: Determine whether the series 3⋅1!/1+32⋅2!/22+33⋅3!/33+…+3n⋅n!/nn+… converges or diverges.

A: Given series is 3·1·1!/1+3·2·2!/2·2+3·3·3!/3·3+…+3·n·n!/n·n To Determine : Whether the above series…

Q: Find the sum of the following series. 2" (a) En=0 Ση-03 m 3n n! 32 33 (b) 1+5 34 +. 4+54 2.52 3+53

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Q: (a) Prove the convergence or divergence of each of the following series: 1! 2! 3! (i) + + +. + n! 2n…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: (a) Determine whether the following series converges or diverges- (r!)³ (3r)! r=1

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Q: Prove that the binomial series a(a – 1) a (a- 1)... (а — п) + | | (1+ x)ª 1+ ax + 2! n! +...…

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Q: n² – 1 > Un where sn = u1 + ... + Un n² + 1 n=1

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Q: b. (− 1)* k² k=1 √kº +1

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Q: Do the series converge absolutely or condition n (2) Σ(-1)^+1 n +3 (b) Σ(-1)"+1 n! 3√√n (c) Σ…

A: Check whether given series converge absolute or conditional.

Q: 1. Describe the convergence of the series 3! + 3² + + (n+1)² (n + 2)! +

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Q: Show that the following series are convergent and find their sums: 1 a) 1ײ×3 +2×3×4 + ... +…

A: (a).

Q: Check the convergence and find the sum of the series: 1 1 1 1 hint.: (2n – 1)(2n + 3) (2n – 1) (2n…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Find the sum of the series. 1 C(-1)"-1. n. 2" 10. 11. Σ-1)" , (7)2n+1 62n+1(2n + 1)! 16 12. 4+ 2! 64…

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