A_(k+1) =(-1)^k*C_15 (k) *(a)^(15 -k)*(b)^k = ||a=x²,b =-3/x³ =-3x^(-3) || =
(-1)^k*C_15 (k) *(x²)^(15 -k)*(-3*x^(-3))^k .
A_(k+1) не содержит x (не зависит от x),если 2(15-k) +k(-3) =0⇒k=6.
---
A_(k+1)=A_(6+1)= a_7 = C_15 6 *(-3)⁶ =3⁶*(15!)/6!(15-6)! =
3⁶*(15*14*13*12*11*10)/(1*2*3*4*5*6)=
3⁶*(15*7*2*13*12*11*2*5)/(15*12*4) =
3⁶*(7*13*11*5) =(9)³*5 *(7*11*13) = 729*5 *1001 =3645*1001.