Chapter 10.4, Problem 18E

Number 9

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

Explain thoroughly please

Attached

True or Flase

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?)

The series (an an+1) converges iff the sequence an converges. (Tips: Cauchy Criterion for Series)

Ode: please correctly and handwritten

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