1/1*1/3+1/3*1/5+1/5*1/7+.1/49*1/51等于多少,
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/09 03:36:25
![1/1*1/3+1/3*1/5+1/5*1/7+.1/49*1/51等于多少,](/uploads/image/z/345825-9-5.jpg?t=1%2F1%2A1%2F3%2B1%2F3%2A1%2F5%2B1%2F5%2A1%2F7%2B.1%2F49%2A1%2F51%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%2C)
x)3727b m
M%H'.tD"}P&m&m==O(OPHjjEBB"b3F".dӽlLMF
Qhd
b$ACi84LH08D& aڸL,
< {ҡ
1/1*1/3+1/3*1/5+1/5*1/7+.1/49*1/51等于多少,
1/1*1/3+1/3*1/5+1/5*1/7+.1/49*1/51等于多少,
1/1*1/3+1/3*1/5+1/5*1/7+.1/49*1/51等于多少,
1/1*1/3+1/3*1/5+1/5*1/7+.+1/49*1/51+...+1/(2n-1)(2n+1)
=1/2[1/1-1/3+1/3-1/5+1/5-1/7+.+1/49-1/51+...+1/(2n-1)-1/(2n+1)]
=1/2[1-1/(2n+1)]
=n/(2n+1)
当n=25时,
1/1*1/3+1/3*1/5+1/5*1/7+.+1/49*1/51+...+1/(2n-1)(2n+1)
=1/1*1/3+1/3*1/5+1/5*1/7+.+1/49*1/51
=25/51
1/1*1/3+1/3*1/5+1/5*1/7+.........1/49*1/51
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+.........1/2(1/49-1/51)
=1/2(1-1/3+1/3-1/5+1/5-1/7+.........+1/49-1/51)
=1/2(1-1/51)
=49/102