a 1=2

a2-a 1=4

a3-a2=6

a4-a3=8

……

An n- an n- 1=2n.

+————

=an=2+4+6+8+....+2n=n(n+ 1)

According to (1),1/an =1/n-1/(n+1)

So 3/A 1+3/A2+3/A3+...3/an = 3( 1/a 1+ 1/A2+...+ 1/an) = 3 [65438]。

The solution is n=20 12.