算式2分之1、6分之1、12分之1、20分之1、30分之1、42分之1、56分之1(简便方法计算)

看不懂,再详细点
2024-12-01 00:24:51
推荐回答(5个)
回答1:

你只需要知道在百度知道里面数学算式都是用计算机语言书写的就能看明白了。1/2就是二分之一,1/3就是三分之一。。。

你的题目里面的加数的分母都可以表示为一个自然数乘以这个自然数加1.

1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
...

规律就是前一项的减数就是后一项的加数,因此可以得到下面这个算法:

1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/(1*2)+1/(2*3)+1/(3*4)+..+1/(7*8)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/7-1/8)
=1-1/2+1/2-1/3+1/3-1/4+..+1/7-1/8
=1-1/8
=7/8

回答2:

注意到 2=2*1
6=3*2
12=4*3
以次类推
并且n(n-1)分之一=(n-1)分之一-n分之一
然后就能简便计算了,结果是8分之7

回答3:

1/2+1/6+1/12+1/20+1/30+/42+1/56
=1-1/2+1/2-1/3+1/3-1/4+...+1/7-1/8
=1-1/8=7/8

回答4:

是1/2+1/6+1/12+1/20+1/30+1/42+1/56=?不
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
---------
1/56=1/7-1/8
结果为7/8。

回答5:

裂相求和!1/2+1/6+1/12+1/20
=1/(1*2)+1/(2*3)+1/(3*4)1/(4*5)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)
=1-1/5=4/5

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