第1章 1.7

(1)

$5,10,20,40,\cdots$

$n=8 \quad a=5 \quad r=2$ より

$S_8 = \dfrac{5(2^8-1)}{2-1} = 1275$

(2)

$12,\pm 6,3,\pm\dfrac{3}{2},\cdots$

$n=8 \quad a=12 \quad r=\pm\dfrac{1}{2}$

$r=\dfrac{1}{2}$のとき

$S_8 = \dfrac{12\left\{\left(\dfrac{1}{2}\right)^8-1\right\}}{1-\dfrac{1}{2}} = \dfrac{765}{32}$

$r=-\dfrac{1}{2}$のとき

$S_8 = \dfrac{12\left\{\left(-\dfrac{1}{2}\right)^8-1\right\}}{1-\left(-\dfrac{1}{2}\right)} = \dfrac{255}{32}$

(3)

$\pm 9,-3,\pm 1,-\dfrac{1}{3},\cdots$

$n=8 \quad a=\pm 9 \quad r=\mp\dfrac{1}{3}$

$r=\dfrac{1}{3}$のとき

$S_8 = \dfrac{-9\left\{\left(\dfrac{1}{3}\right)^8-1\right\}}{1-\dfrac{1}{3}} = \dfrac{3280}{243}$

$r=-\dfrac{1}{3}$のとき

$S_8 = \dfrac{9\left\{\left(-\dfrac{1}{3}\right)^8-1\right\}}{1-\left(-\dfrac{1}{3}\right)} = \dfrac{1640}{243}$

(4)

$2,6,1854,\cdots$

$n=8 \quad a=2 \quad r=3$ より

$S_8 = \dfrac{2(3^8-1)}{3-1} = 6560$