- (a) The given series is alternating. Since
Since ln x is an increasing function,
The series therefore converges.
(b) Since the series converges by the Alternating Series Test, the error in using the first n terms for
the sum of the whole series is less than the absolute value of the (n + 1)st term. Thus the error is
less than Solve for n using
The given series converges very slowly!
(c) The series is conditionally convergent. The given alternating series converges
since the nth term approaches 0 and However, the nonnegative series
diverges by the Integral Test, since
