Question

1/1*3+1/3*5+1/5*7+..+1/（2n+1）（2n+3）=？

Answer 1

1/1*3+1/3*5+1/5*7+..+1/（2n+1）（2n+3）
=(1/2) * { (1-1/3)+(1/3-1/5)+(1/5-1/7)+……+ [ 1/(2n+1)-1/(2n+3) ] }
=(1/2) * { 1-1/3+1/3-1/5+1/5-1/7+……+1/(2n+1)-1/(2n+3) }
=(1/2) * { 1-1/(2n+3) }
=(1/2) * (2n+2)/(2n+3)
=(n+1)/(2n+3)

Answer 2

1/1*3+1/3*5+.......1/(2n-1)*(2n+1)
=1/2(2/1*3+2/3*5.....+2/(2n-1)(2n+1)
=1/2[(3-1)/1*3+(5-3)/3*5+.....+(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)
=n/(2n+1)

追问

大哥 ，，咱能不能别复制，，

你 睁大眼看看，，是一样的题？？？

Answer 3

1/1*3+1/3*5+1/5*7+..+1/（2n+1）（2n+3)
=[1-1/3+1/3-1/5+1/5-1/7+……+1/（2n+1)-1/(2n+3)]/2
=[1-1/(2n+3)]/2
=(n+1)/(2n+3)

追问

明着告诉你，不对！

追答

绝对正确

追问

绝对不对，，3喽的对了！！，

追答

他没有继续化简

追问

我的答案就是他的倒数第2步的这个，，1/2 [ 1-(1/2n+3) ]

追答

你不知道怎样化简就算了
1/2-1/(4n+6) =（n+1)/(2n+3)

Answer 4

1/(2n+1)(2n+3)=1/2*(1/(2n+1)-1/(2n+3))
1/1*3+1/3*5+1/5*7+..+1/（2n+1）（2n+3）=1/2*(1-1/3+1/3-1/5+1/5-1/7+.....1/(2n+1)-1/(2n+3))
=1/2(1-1/(2n+3))=1/2*(2n+2)/(2n+3)=(n+1)/(2n+3)

Answer 5

1/1*3+1/3*5+1/5*7+..+1/（2n+1）（2n+3）
=1/2[(1-1/3)+(1/3-1/5)+(1/5-1/7)+..+(1/（2n+1）-1/（2n+3）)]
=1/2(1-1/3+1/3-1/5+1/5-1/7+..+1/（2n+1）-1/（2n+3))
=1/2[1-1/(2n+3)]
=1/2-1/2(2n+3)
=1/2-1/(4n+6)