Question

$\lim_{n \to \infty} (1+\frac{1}{3}+\frac{1}{3^{2} }+...\frac{1}{3^{n} }) , n$ ∈ N

Answer 1

Explicație pas cu pas:

1+1/3+1/3^2+....+1/n=1/3 * (1-1/3^n)/(1-1/3)=1/3 * 3/2 * (3^n-1)/3^n=>lim[(3^n -1)/(2*3^n)]=1/2