45.46.1 − x + a 2 x^2 + a 3 x^3 + · · · = − (−1 + 2a 2 x + 3a 3 x^2 + 4a 4 x^3 + · · ·)
identically. Thus,It is clear, then, that(D) Use a calculator to verify that the ratio (of the given geometric
series) equals approximately 0.98. Since the ratio r < 1, the sum of the
series equals
or Simplify to get (D).(A) Since the given series converges by the Alternating Series Test, the
error is less in absolute value than the first term dropped, that is, less than. Choice (A) is closest to this approximation.