3.
5.
6.
8.
Part A
(A) The series is geometric with a = and r = ; it
converges to
(C) is the sum of an infinite geometric series with first term 1 and
common ratio −2x. The series is 1 − 2x + 4 x^2 − 8x^3 + 16 x^4 − · · · ·
(B) Assume that Then 2x + 3 = A(x − 2) + B(x
− 1). Because all the choices have a denominator of x − 1, you are
looking for A, so let x = 1:
2(1) + 3 = A(1 − 2); A = −5
(A) Using the Ratio Test, we get
convergent.
does not exist and thus the series
diverges because it doesn’t pass the nth term test.
III. We would like to compare this series with however, we cannot
use the Comparison Test because (see note below). So we must
use the Limit Comparison Test: Since
also diverges by the Limit Comparison Test.
