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:2024/08/28 09:56:50
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