Question

Determine a soma dos (20) primeiros elementos da progressão geométrica (2, 8, 32, 128, ...).

Answer 1

$q=\dfrac82=4\\\\a_1=2\\\\n=20\\\\\\S_n=\dfrac{a_1(q^n-1)}{q-1}\\\\\\\dfrac{2(4^{20}-1)}{4-1}=\\\\\\\dfrac{2(1099511627776-1)}{3}=\\\\\\\dfrac{2(1099511627775)}{3}=2(366503875925)=\boxed{733007751850}$