This is a series that I could use some help with solving. Could I get some help solving this series please? Thanks much!!!

Question

b. How many terms are needed to approximate this series to within 0.000001? Find the approximate value to within 0.000001.

c. Determine is this series if absolutely or conditionally convergent.

Answer 1

The series converges absolutely by the ratio test.

To find the number of terms needed, you need to calculate the value of the first term, less than10^-6

^{As far as I know there is no EASY way to do that except to calculate values for k starting with some big number and work in whichever direction you need to go...you could I guess use the Simpson approximation to the factorial, but it won't help much. or even a table of factorials will be a help.}