10. Σ=1 2n²+4n+1 n³+9

Q: (-1)^arctan n in=1

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Q: +o0 а. n п+2 n=1

A:

Q: ηλη Σ (2η)! n=1

A: The given series .The aim is to determine whether the given series is converges or diverges.Ratio…

Q: 3 (4 3 (4 Σ 4 k=1 7 9.

A:

Q: 6. 5. Σ m(n+2) In 1 6. Σ 7. E 5 7+1

A: In 5 and 6 using comparison test while in 7 using D'Aembert Ratio test.

Q: 4h 2. E+3 (-1)"3 3. E 4. E常 e" 6. 5. 5

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 7" (d) 8" n=5 4" (e) E 4"+4 7" + 3" 8" n=1

A: The above series are

Q: Determine if the series converges or diverges. Give a reason for your answer. 5 - Σ n5"

A: Calculate as following:-

Q: Evaluate the series or state that it diverges.

A: Given that : The series ∑k =0∞  116k2 + 8k - 3 . First factoring the denominator term,…

Q: 22n + 2" +1 (-1)* 1. 4n + 3n +5 n=1

A: Given: ∑n=1∞-1n22n+2n+14n+3n+5 To determine: Whether the given series is convergent or divergent.

Q: cos(nt) 4 (In n) n=2

A: The series is given as , ∑n=2∞cosnπln n4

Q: 18. Show that Σkind(k)³ = (Σk|n d(k))² for all positive integer n.

A:

Q: 00 2n+4" (1) E n=1n+6"+1 (2) En ( 3) Σ cos [(2n+1)!]? (1-2n)" 00 00 1 (4) E n" (5) E arctan n n=1

A:

Q: 1 (ii) 2n=2 13+1 100

A:

Q: n=1 ,2n TO

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Q: Determine whether the series converges or diverges. 9 +3" 2" n= 1 converges diverges

A:

Q: Determine whether the series is convergent or divergent. 5 3 7n n 1 convergent divergent If it is…

A: Given series is,

Q: 7 立。 3" 6 ) 5) 4) Ž 9 +2^ n! n+1 n=1

A: Limit test:  If the limit of sequence approaches to any finite number then the series is convergent…

Q: 2n²(-1)" En=1 3n2+4n+1

A: given series is                                                         ∑n=1∞2n2(-1)n3n2+4n+1…

Q: ∞ (d) Ene-n? n=1

A: We have to determine whether the series converges or diverges.…