Free-Response
Part A
- (a) Use the Ratio Test:
The radius of convergence is 1. At the endpoint x = 1,
Since
this series converges by the Alternating Series Test. Thus converges for
positive values 0 < x ≤ 1.
(b) Because satisfies the Alternating Series Test, the error in approximation
after n terms is less than the magnitude of the next term. The calculator shows that at
n = 5 terms.
(c) is a negative series. Therefore the error will be larger than the
magnitude of the first omitted term, and thus less accurate than the estimate for f (0.5).
