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. 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.