(x+1)(x+2)⋯(x+999)1
The partial fraction decomposition of the expression above can be expressed as m=1∑999x+mam for some a1,a2,…,a999.
If max{∣a1∣,∣a2∣,…,∣a999∣}=(Q!)21, find Q.
Notations:
- ∣⋅∣ denotes the absolute value function.
- ! denotes the factorial notation. For example, 8!=1×2×3×⋯×8.