S=q+2q^2+...+nq^n qS= q^2+...+(n-1)q^n+nq^(n+1) (1-q)S=q+q^2+...+q^n-nq^(n+1) =q(1-q^n)/(1-q)-nq^(n+1) =>S=q(1-q^n)/(1-q)^2-nq^(n+1)/(1-q) 当n逼近于正无穷时 S=q/(1-q)^2
