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