在线段AB上取1个点,共有3条线段；取2个点,共有6条线段；取3个点,共有10条线段；...取n个点,共多少线段好纠结

在线段AB上取1个点,共有3条线段；取2个点,共有6条线段；取3个点,共有10条线段；...取n个点,共多少线段好纠结
在线段AB上取1个点,共有3条线段；取2个点,共有6条线段；取3个点,共有10条线段；...取n个点,共多少线段
好纠结

在线段AB上取1个点,共有3条线段；取2个点,共有6条线段；取3个点,共有10条线段；...取n个点,共多少线段好纠结
1)线段AB上取1个点时:
由2条线段组成的线段为AB,由1条线段构成的线段有2条,故共有(1+2)条;
2)线段AB上取2个点时:
最长线段是由3条线段组成的线段即AB,由2条线段组成的线段有2条,由1条线段构成的线段为3条.
故共有:(1+2+3)条;
3)线段AB上取3个点时:
由以上规律可知,共有线段:(1+2+3+4)条;
……
所以,线段AB上取n个点时:共有线段:1+2+3+…+（n+1)=(n+2)(n+1)/2(条）.

应该是（n+2）（n+1）/2 取一个点是 2+1 取两个点是3+2+1 取3个点是4+3+2+1 。。。。然后就有规律了 n个点就是1 +2+3+4+5+...加到n+1 答案就是(n+1)(n+2)/2

取1个点 线段数 （1+2）*（1+2-1）/2=(1+2)*(1+1)/2=3
取2个点 线段数 （2+2）*（2+2-1）/2=(2+2)*(2-1)/2=6
取3个点 线段数 （3+2）*（3+2-1）/2=(3+2)*(3+1)/2=10
取n个点 线段数 （n+2）*（n+2-1）/2=（n+2)*(n+1)/2
其实相当于 n+2个人握手 ，每人相互...

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取1个点 线段数 （1+2）*（1+2-1）/2=(1+2)*(1+1)/2=3
取2个点 线段数 （2+2）*（2+2-1）/2=(2+2)*(2-1)/2=6
取3个点 线段数 （3+2）*（3+2-1）/2=(3+2)*(3+1)/2=10
取n个点 线段数 （n+2）*（n+2-1）/2=（n+2)*(n+1)/2
其实相当于 n+2个人握手 ，每人相互握一次，共握多少次？
那么 每人握 n+1次，共握（n+2)(n+1)次 因为2人互握有重复，所以除以2 得（n+2)*(n+1)/2

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n
sajjm

（n+2)*(n+1)/2 我们老师刚讲过 可恶的他竟然说这道题不会的是白痴。。。

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1)线段AB上取1个点时:
由2条线段组成的线段为AB,由1条线段构成的线段有2条,故共有(1+2)条;
2)线段AB上取2个点时:
最长线段是由3条线段组成的线段即AB,由2条线段组成的线段有2条,由1条线段构成的线段为3条.
故共有:(1+2+3)条;
3)线段AB上取3个点时:
由以上规律可知,共有线段:(1+2+3+4)条;
……

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1)线段AB上取1个点时:
由2条线段组成的线段为AB,由1条线段构成的线段有2条,故共有(1+2)条;
2)线段AB上取2个点时:
最长线段是由3条线段组成的线段即AB,由2条线段组成的线段有2条,由1条线段构成的线段为3条.
故共有:(1+2+3)条;
3)线段AB上取3个点时:
由以上规律可知,共有线段:(1+2+3+4)条;
……
所以,线段AB上取n个点时:共有线段:1+2+3+…+（n+1)=(n+2)(n+1)/2(条）。

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