证明：当n=1时,明显有1/(1×3)=1/(2×1+1)成立,则原式成立.假设当n=k时,有1/1×3+1/3×5+...+1/(2k-1)(2k+1)=k/2k+1成立,则当n=k+1时,1/1×3+1/3×5+...+1/(2k-1)(2k+1）+1/(2(k+1)-1)(2(k+1)+1)=k/2k+1 + 1/(2k+1)(...