强化一下证明1/(2*3)+1/(3*5)+1/(4*7)+.1/((n+1)*(2n+1))≤5/12-1/(2n+2)n=1时 显然若 n=k-1时成立 n=k时左≤5/12-1/(2k)+1/((k+1)*(2k+1))≤5/12-1/(2k)+1/((k+1)*(2k))=5/12-1/(2k+2)所以.