Question

Quanto vale o produto (a)(aq)(aq2)(aq³)...(aqn
-1)?
(A) a.qn
(B) a.qn -1
(C) an.qn – 1
(D) an.qn(n - 1)/2

Answer 1

Olá, Rsmattosjr.

$a\cdot aq\cdot aq^2\cdot aq\³\cdot ...\cdot aq^{n-1}=\\\\ =\underbrace{a\cdot...\cdot a}_{n\text{ vezes}}\cdot q^0\cdot q^1\cdot q^2\cdot q^3\cdot ...\cdot q^{n-1}=\\\\\\ =a^nq^{0+1+2+3+...+n-1}=\\\\ =a^nq^{n\cdot\frac{(0+n-1)}2}=\\\\ =a^nq^{\frac{n(n-1)}2}$

Resposta: letra "D"