化简X-X^2-X^3-X^4-...X^9+X^10

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 21:10:27
化简X-X^2-X^3-X^4-...X^9+X^10

化简X-X^2-X^3-X^4-...X^9+X^10
化简X-X^2-X^3-X^4-...X^9+X^10

化简X-X^2-X^3-X^4-...X^9+X^10
令s=X^2+X^3+……+X^9
Xs=X^3+X^4+……+X^9+X^10
Xs-s=X^10-X^2
S=(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-X)/(X-1)

回答不了你
这里面很多符号没有
表达不出来
很抱歉

怎么最后一个是加号？^符号是除号吗？

当x=1时,
原式=-8.
当x≠1时,
原式=x-(x^2+x^3+x^4+...x^9)+x^10
=x-x^2(1-x^8)/(1-x)+x^10
=(x-2x^2+2x^10-x^11)/(1-x).

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