1/1X3+1/3X5+1/5X7+……+1/(2n-1)(2n+1)=?虽然我知道了答案是n/2n+1,_数学解答

1/1X3+1/3X5+1/5X7+……+1/(2n-1)(2n+1)=?
虽然我知道了答案是n/2n+1,

人气：198 ℃　时间：2020-07-18 06:06:02

解答

1/1X3+1/3X5+1/5X7+……+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/(2n+1)
=n/(2n+1)