51问答网 > 1+1⼀2+1⼀(1+2+3)+.......+1⼀(1+2+3+......100)=?

1+1⼀2+1⼀(1+2+3)+.......+1⼀(1+2+3+......100)=?

2025-02-23 22:39:38

推荐回答（3个）

回答1：

题打错了吧1+1/2+【1/（1+2）】+ 1/(1+2+3)+.......+

1/an=1/[(1+n)*n/2]=2/(1+n)*n=2/n-2/(n+1); n=1,2,……，100
Sn=1+1/2++1/（1+2）+1/(1+2+3)+.......+1/(1+2+3+......100)
=2/1-2/2+2/2-2/3+2/3-2/4+……+2/100-2/101
=2-2/101
=200/101

回答2：

1/an=1/[(1+n)*n/2]=2/(1+n)*n=2/n-2/(n+1); n=1,2,……，100
Sn=1+1/2++1/（1+2）+1/(1+2+3)+.......+1/(1+2+3+......100)
=2/1-2/2+2/2-2/3+2/3-2/4+……+2/100-2/101
=2-2/101
=200/101

回答3：

=1+1/2+1/6+1/10+1/15+1/21+...+1/5050
=1+1/2+2(1/12+1/20+1/30+1/42+...+1/10100)
=1+1/2+2(1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7...+1/100-1/101)
=1+1/2+2(1/3-1/101)
=1+1/2+2/3-2/101
=1301/606