(1 -1/3 +1/3² -1/3³ +...-1/3²⁰¹¹)/(1 -1/3²⁰¹²) (observam ca termenii sumei formeaza o progresie geometrica de ratie q=-1/3 => S=b₁·(qⁿ -1)/q-1 =1·((-1/3)²⁰¹² -1)/-1/3 -1) =(1/3)²⁰¹² -1 /-4/3 /(3²⁰¹² -1 /3²⁰¹²)=(-3/4)·(1/3)²⁰¹² ·3²⁰¹² /(3²⁰¹² -1)=(-3/4)/(3²⁰¹² -1) .
