Question

Calcule a soma dos termos da seguinte sequência PG $(-3, -1, -\frac{1}{3} , -\frac{1}{9}, ...)$

Answer 1

Seja K o valor dessa soma.

$k = -3 -1-\dfrac{1}{3} -\dfrac{1}{9}-\cdots\\\\\\-k = +3 +1+\dfrac{1}{3} +\dfrac{1}{9}+\cdots\\\\\\ -\dfrac{k}{3} = 1+\dfrac{1}{3} +\dfrac{1}{9}+\cdots\\\\\\ \dfrac{k}{3} = -1-\dfrac{1}{3} -\dfrac{1}{9}-\cdots\\\\\\\dfrac{k}{3}-k = 3\\\\\\-\dfrac{2k}{3}=3\\\\\\k = -\dfrac{9}{2}$