How to solve the following sum?
$$\sum_{n=0}^k (-1)^n (1/2)^n$$
Answer
use the geometric serie for $|x|<1$
$$\sum_{n=0}^{k }x^n=1+x+x^2+x^3+....=\frac{1-x^{k+1}}{1-x}$$
then use $x=-1/2$
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