Chapter 10.4, Problem 14E

Help solving problem and finding interval

What is the radius of convergence for the power series (see image)

Can you show me how to solve this?

Analyze the behaviour of the power series n=0 and techniques. n(x+3)" 5" by using appropriate theorems

7. Consider the power series (-1)*+1g" n2 n=1 (a) The series converges when |x| R. Find R. (b) Does the series converge when x = R? What about when x = -R? Explain.

Preso FIN- 45 32. Determine whether the following series converges absolutely, converges conditionally, or diverges. 8 71=1 (-1)" (n³+2n²-1) n7/2+3+1

In the image below.

Give an example of an increasing sequence {an} that converges to 12. What can you conclude about the series En=1an? (Does it converge or diverge?) Give an example of a series that converges to 12. What can you conclude about the sequence {an}? (Does it converge or diverge?)

a,c, d,f please i need so much help