1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4,...根据以上规律计算下面的题目:1/6+1/12+1/20+1/30+1/42+1/56+1/72=?你们怎么都没有打小括号呀?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/20 15:38:41
![1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4,...根据以上规律计算下面的题目:1/6+1/12+1/20+1/30+1/42+1/56+1/72=?你们怎么都没有打小括号呀?](/uploads/image/z/2087830-46-0.jpg?t=1%2F2%3D1-1%2F2%2C1%2F6%3D1%2F2-1%2F3%2C1%2F12%3D1%2F3-1%2F4%2C...%E6%A0%B9%E6%8D%AE%E4%BB%A5%E4%B8%8A%E8%A7%84%E5%BE%8B%E8%AE%A1%E7%AE%97%E4%B8%8B%E9%9D%A2%E7%9A%84%E9%A2%98%E7%9B%AE%3A1%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B1%2F42%2B1%2F56%2B1%2F72%3D%3F%E4%BD%A0%E4%BB%AC%E6%80%8E%E4%B9%88%E9%83%BD%E6%B2%A1%E6%9C%89%E6%89%93%E5%B0%8F%E6%8B%AC%E5%8F%B7%E5%91%80%EF%BC%9F)
1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4,...根据以上规律计算下面的题目:1/6+1/12+1/20+1/30+1/42+1/56+1/72=?你们怎么都没有打小括号呀?
1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4,...根据以上规律计算下面的题目:1/6+1/12+1/20+1/30+1/42+1/56+1/72=?
你们怎么都没有打小括号呀?
1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4,...根据以上规律计算下面的题目:1/6+1/12+1/20+1/30+1/42+1/56+1/72=?你们怎么都没有打小括号呀?
1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/2-1/9
=7/18
1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/2-1/9
=7/18
根据规律得:
1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/2-1/9
=7/18
1/6 = 1/2 - 1/3
1/12 = 1/3 - 1/4
1/20 = 1/4 -1/5
1/30 = 1/5 -1/6
1/42 = 1/6 - 1/7
1/56 = 1/7 - 1/8
1/72 = 1/8 - 1/9
1/6+1/12+1/20+1/30+1/42+1/56+1/72
=(1/2 - 1/3) + (1/3 - 1/4 )+ (1/4 -1/5 )+ (1/5 -1/6) + (1/6 - 1/7) + (1/7 - 1/8) +(1/8 - 1/9)
=1/2 - 1/9
=7/18
原式=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)
+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)
=1/2-1/9
=4/9
=1/2 - 1/3 + 1/3 - 1/4 + 1/4-1/5 +1/5 -1/6 +1/6- 1/7 +1/7 -1/8+1/8 -1/9
=1/2-1/9
=7/72
这个题需要先求出1/72=1/8-1/9,题目1/6+1/12+1/20+1/30+1/42+1/56+1/72=1/2-1/9=7/18.
1/6+1/12+1/20+1/30+1/42+1/56+1/72
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/2-1/9
=7/18