Question

calcule o limite da soma (1 + 1/2 + 1/4 + 1/8 + ...) + (1 + 1/3 + 1/9 + 1/27 + ...)​

Answer 1

Resposta:

Explicação passo-a-passo:

Trata-se da soma de duas progressões geométricas (PG) infinitas cuja fórmula é:

$S=\dfrac{a1}{1-q}$

então teremos

$S1+S2=\dfrac{1}{1-\frac{1}{2}}+\dfrac{1}{1-\frac{1}{3}}\\\\\\S1+S2=\dfrac{1}{\frac{2-1}{2}}+\dfrac{1}{\frac{3-1}{3}}\\\\\\S1+S2=\dfrac{1}{\frac{1}{2}}+\dfrac{1}{\frac{2}{3}}\\\\\\S1+S2=2+\dfrac{3}{2}\\\\\\S1+S2=\dfrac{4+3}{2}\\\\\\S1+S2=\dfrac{7}{2}$