化简X-X^2-X^3-X^4-...X^9+X^10
问题描述：
化简X-X^2-X^3-X^4-...X^9+X^10
答
令s=X^2+X^3+……+X^9Xs=X^3+X^4+……+X^9+X^10Xs-s=X^10-X^2S=(X^10-X^2)/(X-1)所以原式=X-s+X^10=X+X^10-(X^10-X^2)/(X-1)=[(X^10+X)(X-1)-(X^10-X^2)]/(X-1)=(X^11-X^10+X^2-X-X^10+X^2)/(X-1)=(X^11-2X^10+2X^2-...