If the coefficient of x^30 in the expansion of (1+1x)^6(1+x^2)^7(1-x^3)^8, x0, is , then |…

Question

If the coefficient of $x^{30}$ in the expansion of $\left(1+\dfrac1xight)^6(1+x^2)^7(1-x^3)^8$, $x
e0$, is $\alpha$, then $|\alpha|$ equals\_\_\_\_\_\_

Answer: 678

Accepted Answer

Combining contributions across all three factors that yield $x^{30}$ terms:

$$\text{Coeff.} = 7+(15\times21)+(15\times35)+35-(6\times8)-(20\times7\times8)-(6\times21\times8)+(15\times28)+(7\times28)=-678=\alpha$$

$$|\alpha|=678$$

Solutions · 1