已知(1-1/2)×1的平分=1/2 (1/2-1/3)×2的平分=2/3 (1/3-1/4)×3的平分=3/4,用含n的等式,写出规律,证明

已知(1-1/2)×1的平分=1/2 (1/2-1/3)×2的平分=2/3 (1/3-1/4)×3的平分=3/4,用含n的等式,写出规律,证明

[1/n-1/(n+1)]n²=n/(n+1)
左边=n²/n-n²/(n+1)
=n-n²/(n+1)
=(n²+n-n²)/(n+1)
=n/(n+1)