证明:(1)当n=1时,n(n+1)(2n+1)＝1*(1+1)(2*1+1)=6 显然能被6整除 设n=k时,k(k+1)(2k+1)能被6整除 当n=k+1时,(k+1)[(k+1)+1][2(k+1)+1] =(k+1)(k+2)(2k+3) =(k+1)k(2k+3)+2(k+1)(2k+3)...