1/(2x2-1)+1/(4x4-1)+1/(6x6-1)+-----+1/(100x100-1)=

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 20:51:32

1/(2x2-1)+1/(4x4-1)+1/(6x6-1)+-----+1/(100x100-1)=
1/(2x2-1)+1/(4x4-1)+1/(6x6-1)+-----+1/(100x100-1)=

1/(2x2-1)+1/(4x4-1)+1/(6x6-1)+-----+1/(100x100-1)=
1/(n^2-1)=1/2[1/(n-1)-1/(n+1)]
原式=1/2[1-1/3+1/3-1/5+.+1/99-1/101]
=1/2(1-1/101)
=50/101