1/(x-1)x+1/x(x+1)+…+1/(x+9)(x+10)=11/12

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/27 02:14:44
1/(x-1)x+1/x(x+1)+…+1/(x+9)(x+10)=11/12
x)3ר5Ԭ6ԯڏiD-5AF6IE$/!^鞆gº@3odϞs6@<7ٚO'ghxp^gxkҳ϶u<7a$#t^6zVU,w3΋勁j+lu uLz 1{

1/(x-1)x+1/x(x+1)+…+1/(x+9)(x+10)=11/12
1/(x-1)x+1/x(x+1)+…+1/(x+9)(x+10)=11/12

1/(x-1)x+1/x(x+1)+…+1/(x+9)(x+10)=11/12
1/(x-1)x可以拆开成1/(x-1)-1/x.类似地可以依次拆开后面的每一项,前后项相互抵消,得1/(x-1)-1/(x+10)=11/12,通分,得11/(x-1)(x+10)=11/12即(x-1)(x+10)=12,解得x=-11或x=2