Summer II 2016 Exam 3 Determine whether the series is absolu

Summer II 2016 Exam 3 Determine whether the series is absolutely convergent, conditionally convergent, or divergent. You must justify your conclusion, including any tests used and evidence that the requirements of the tests are met. (-1)\" In n 10. n 1

Solution

1) We will use Alternating series test .

(ln n )/n goes to 0 as n goes to infinty and also ln/n is a decreasing sequence.

hence it satisfies all conditions in Alternative series test. And hence it is absolutely convergent.

2)4^n/(n^2 n!) is less than 1/n^2 for large n .

this test is the sandwich test

series Sum(1/n^2) is convergent

hence it is convergent