Answer
A. 1533
B. 510
C. 4923
D. 9842
Work Step by Step
A. This is a geometric progression with its initial value is 3 and ratio 2. Then, by the formula of geometric series, we can obtain that
$3 + 3 * 2 + … + 3 * 2^{8} = 3 * \frac{2^{9} -1}{2-1} = 1533.$
B. By the formula of geometric series,
$2 + 2^{2} + 2^{3} + … + 2^{8} = 2* \frac{2^{8}-1}{2-1} = 510.$
C. $(-3)^{2} + (-3)^{3} + (-3)^{4} +...+ (-3)^{8} = 9-27+81-243+729-2187+6561 = 4923.$
D. From answer C, we can obtain
$\sum_{j=0}^{8} (-3)^{j} = 1 - 3 + 4923 = 4921$.
Then, the result is
$ 2 * 4923 = 9842. $
