1/1乘3+1/3乘5..+1/（2n-1)(2n+1）=?想问为甚要除以二?上述得出的规律都不用啊?在下实属愚钝.1/1×3+1/3×5+1/5×7+…+1/(2n-1)(2n+1)=1/2(1-1/3+1/3-1/5+1/5-1/7+.+1/2n-1-1/2n+1)=1/2(1-1/2n+1)=1/2(2n+1-1/2n+1)

Question

1/1乘3+1/3乘5..+1/（2n-1)(2n+1）=?想问为甚要除以二?上述得出的规律都不用啊?在下实属愚钝.
1/1×3+1/3×5+1/5×7+…+1/(2n-1)(2n+1)
=1/2(1-1/3+1/3-1/5+1/5-1/7+.+1/2n-1-1/2n+1)
=1/2(1-1/2n+1)
=1/2(2n+1-1/2n+1)

Answer 1

因为1-1/3=2/1×3（通分相减）
1/3-1/5=2/3×5
……
而题目是1/1×3+1/3×5+1/5×7+…+1/(2n-1)(2n+1)
所以(1-1/3+1/3-1/5+1/5-1/7+.+1/2n-1-1/2n+1)只有乘1/2才能与题目相等