lim n箭头无限大【1/1.3+1/3.5+……+1/(2n-1)(2n+1)】怎么算

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/02 22:14:23
lim n箭头无限大【1/1.3+1/3.5+……+1/(2n-1)(2n+1)】怎么算

lim n箭头无限大【1/1.3+1/3.5+……+1/(2n-1)(2n+1)】怎么算
lim n箭头无限大【1/1.3+1/3.5+……+1/(2n-1)(2n+1)】怎么算

lim n箭头无限大【1/1.3+1/3.5+……+1/(2n-1)(2n+1)】怎么算
因为1/(2n-1)(2n+1)
=1/2*(1/(2n-1)-1/(2n+1))
则1/1.3+1/3.5+……+1/(2n-1)(2n+1)
=1/2*(1-1/3+1/3-1/5+……+1/(2n-1)-1/(2n+1))
=1/2*(1-1/(2n+1))
则极限为1/2