a1b1+a2b2+…+anbn
=a1L1+c2L2+c3L3+…+ckLk+…+cnLn
=c1L1+c2L2+c3L3+…+ckLk+…+cnLn
=c1（b1+b2+…+bn）+c2(b2+b3+…+bn)+c3(b3+b4+…+bn)+...+ck(bk+b(k+1)+...+bn)+...+cnbn
=b1c1+b2(c1+c2)+b3(c1+c2+c3)+...+bk(c1+c2+...+ck)+...bn(c1+c2+...+cn)
等式两边b1,b2,b3...bn对应系数相等
∴a1=c1,a2=c1+c2,...ak=c1+c2+...+ck,.an=c1+c2+...+cn
∴ak-a(k-1)=(c1+c2+...+ck)-(c1+c2+...+c(k-1))=ck
即ck=ak-a(k-1) （2≤k≤n）