2. Determine if the series is convergent or divergent. (a) (b) (c) k=1 6.8.10. 4.7.10 k=2 k=1 (sink) . (k!)² (2k)! (2k + 4) (3k + 1) k³ lnk + k + 1 k5+ k³ + 1

Q: 6. Are the following series convergent? Why? (a). (b) 00 n=1 α 2 (3n-1)1.3 n=1 n2 – 1 2η2 + η

A: The given series are ,  (a).        ∑n=1∞2(3n-1)1.3 (b).         ∑n=1∞ n2-12n2+n (.)  Necessary…

Q: 1. Show that the series (-1)-1 (3n+5) In(n+2)+3 is convergent, and determine how many terms of the…

A: Given that the series    ∑n=1∞(-1)n1(3n+5)ln(n+2)+33

Q: α. 3 n Σ 4 n=1 |

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The series obtained by differentiating term by term the series (x- 2), (x-2)', (x – 2)* | (x - 2) +…

A:

Q: 3. Decide whether each or not of the following series converges. (k + 1)4* * k=0 k(-2)* と2k-1(k +1)!…

A: To decide whether each of the following series convereges or not.

Q: Consider the series (-1)" (6x+5)" n=0 (a) Find the series' radius and interval of convergence. (b)…

A: We have to find- series radius and interval of convergence, values of x for which series converge…

Q: 3) For the geometric series 4 + 16x - 4 + 64x2 -16+ ... Find the range of values of x for which the…

A: We have to find the range of 'x' for whichGeometric series 4+(16x-4)+(64x2-16)+··········· converges

Q: 3. Find the interval of convergence of the given series. Show your work! (x- 7)" 27 (n2 + 1) n=0

A: Explanation of the answer is as follows

Q: 5). Determine whether the series converges or diverges. ∞ n + ln(n) n2 + 17n − 12 n = 1 Which…

A:

Q: P4. Determine whether the given series are a) absolutely convergent, b) conditionally (ii) 2 –+…

A: To determine whether the below series are absolutely convergent, conditionally convergent, or…