设Sn=1+(-1/3)+(-1/3)^2-...+(-1/3)^n =(-1/3)[1-(-1/3)^n]/(1+1/3)+1 =3/4+(-1/3)^n当n→∞时，Sn→3/4所以lim〔1-1/3+1/3^2-...+(-1/3)^n〕=3/4
