According to the meaning of the problem, an important identity-Abel formula is found by using their area relationship:

a 1b 1+a2 B2+a3 B3+…+anbn = a 1(b 1-B2)+L2(B2-B3)+L3(B3-B4)+…+Ln- 1(bn- 1-bn)+Lnbn、

When n=2, then a1b1+a2b2 = a1(b1-b2)+l2b2,

∴L2=a 1+a2，

When n=3, then a1b1+a2b2+a3b3 = a1(b1-b2)+l2 (b2-b3)+l3b3,

∴L3=a 1+a2+a3，

Generalize this conclusion, LN = A 1+A2+A3+…+An.

So the answer is: a 1+a2+a3, A 1+A2+A3+…+An.