Σ(−1)n n² + 2n + 3 5η3 + n + 1 n=1 11.

Q: u) 1 Σ(-3 ---) n

A: Convergence of the series is tested by using comparison test

Q: (2k – 1)(k² – 1) (k + 1)(k² + 4)² - k=1 d.

A:

Q: n52n n+1 n=1

A: The given series is ∑n=1∞n52n10n+1 which is of the form ∑n=1∞an where an=n52n10n+1. Obtain an+1 as…

Q: 8 n = 1 2n +7" 14"

A:

Q: determine whether the series is absolutely convergent, conditionally convergent, or divergent.

A:

Q: Determine the behavior of the following SERIES. (4n²+5)" (3n+ 1)2n The series n=1 The series Σ(-1)",…

A: To Determine: The behavior of the following SERIES. 1. ∑n=1∞4n2+5n3n+12n 2. ∑n=1∞-1n 1ln n 3.…

Q: (d) 22n+1 п! n=1 (e) (-1)" arctan (n) Σ n2 n=1

A: We have to determine whether the series is absolutely convergent, conditionally convergent,or…

Q: series is convergent or divergent.

A:

Q: Determine whether the series converges or diverges.

A:

Q: 33. COS пл Зп + 2 n = 1 8 W

A: Given series ∑n=1∞cosnπ3n+2. The objective is to determine whether the series is absolutely…

Q: Determine whether the series converges or diverges.

A:

Q: E(-1)" (Зп — 1)! 5"(n!) n=1

A:

Q: Determine whether the series is convergent or divergent.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Determine whether the series converges or diverges.

A:

Q: determine if the series is absolutely convergent, conditionally convergent, or divergent.

A:

Q: k sin?k 1 + k3

A: Let, ak=ksin2k1+k3