1⼀1*3+1⼀3*5+1⼀5*7+......+1⼀49*51怎么算啊？急急急急急啊 要详细的呦O(∩_∩)O~

1/1×3+1/3×5＋1/5×7+…＋1/49×51

=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]

=1/2×50/51

=25/51

原式等于1/2(1-1/3+1/3-1/5......+1/49-1/51)
=1/2(1-1/51)
=25/51

解：
1/1*3=(1/2)×(1/1-1/3)
1/3*5=(1/2)×(1/3-1/5)
1/5*7=(1/2)×(1/5-1/7)
...
1/49*51=(1/2)×(1/49-1/51)

1/1*3+1/3*5+1/5*7+......+1/49*51
=(1/2)×(1/1-1/3+1/3-1/5+1/5-1/7+....+1/49-1/51)
=(1/2)×(1/1-1/51)
=(1/2)×50/51
=25/51

解析：

1/[n(n+2)]=(1/2)[(n+2)-n]/[n(n+2)]=(1/2)[1/n-1/(n+2)]

∴原式

=(1/2)*[1-1/3+1/3-1/5+1/5-1/7+…………+1/49-1/51]

=(1/2)*[1-1/51]

=(1/2)*50/51
=25/51
不懂欢迎再问

谢谢

好了