化简:1/X(X+1) +1/(X+1)+(X+2) +1/(X+2)(X+3) +.+1/(X+2006)(X+2007)

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/10 08:15:25

化简:1/X(X+1) +1/(X+1)+(X+2) +1/(X+2)(X+3) +.+1/(X+2006)(X+2007)
化简:1/X(X+1) +1/(X+1)+(X+2) +1/(X+2)(X+3) +.+1/(X+2006)(X+2007)

化简:1/X(X+1) +1/(X+1)+(X+2) +1/(X+2)(X+3) +.+1/(X+2006)(X+2007)
运用裂项相消的办法,例如1/x(x+1)=1/x-1/(x+1),后面运用同样的方法完成.最后2007/x(x+2007)

答案最后等于1/x-1/(x+2007)

1/X(X+1)+1/(X+1)(X+2)+1/(X+2)(X+3)+…+1/(X+2006)(X+2007)
=1/X-1/(X+1)+1/(X+1)-1/(X+2)+1/(X+2)-1/(X+3)+…+1/(X+2005)-1/(X+2006)+1/(X+2006)-1/(X+2007)
=1/X-1/(X+2007)