When n = 1, the inequality of left = 3/5 and right = 1/2 holds.

When n = 2, the inequality of left = 3/5+9/ 1 1 = 78/55 and right =8/9 holds.

When n = 3, the left side = 2.349, and the right side = 17/ 16, the inequality also holds.

The following should be the integer n > 3, and the inequality is also true.

The fraction on the right side of the inequality can be arranged as 3/2-3/[2 (n+1)]-1/(n+1) 2.

When n > 3 points, a1+A2+...+An > A1+A2+A3 = 2.349 > 3/2 >？ 3/2-3/[2(n+ 1)]- 1/(n+ 1)^2

So inequality is established.