need help with geometric series

Question

could any one give me hint how to solve $$\sum_{n=1}^\infty \frac{3}{(-2)^n} $$

using the geometric series?

Answer 1

Write

$$ 3 \sum_{n \geq 1} \left( \frac{-1}{2} \right)^n = 3 \sum_{n \geq 0} \left( \frac{-1}{2} \right)^n - 3 = 3 \cdot \frac{ 1 }{1 + \frac{1}{2}} -3 = 3 \cdot \frac{2}{3} - 3 = -1$$