Answer
(a) $-\frac{3}{2}$
(b) $-\frac{5}{4}$
(c) $-\frac{11}{8}$
Work Step by Step
$\displaystyle \sum_{n=1}^{∞}4(-\frac{1}{2})^n$
(a) $4(-\frac{1}{2})^1+4(-\frac{1}{2})^2+4(-\frac{1}{2})^3=-2+1-\frac{1}{2}=-\frac{3}{2}$
(b) $4(-\frac{1}{2})^1+4(-\frac{1}{2})^2+4(-\frac{1}{2})^3+4(-\frac{1}{2})^4=-2+1-\frac{1}{2}+\frac{1}{4}=-\frac{5}{4}$
(c) $4(-\frac{1}{2})^1+4(-\frac{1}{2})^2+4(-\frac{1}{2})^3+4(-\frac{1}{2})^4+4(-\frac{1}{2})^5=-2+1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}=-\frac{11}{8}$
