2x3/1+3×4/1+4×5/1……+99×100/1的规律计算
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解决时间 2021-02-06 10:33
- 提问者网友：我是女神我骄傲
- 2021-02-05 15:56
2x3/1+3×4/1+4×5/1……+99×100/1的规律计算
最佳答案
- 五星知识达人网友：洒脱疯子
- 2021-02-05 16:33
1/(2×3)=(3-2)/(2×3)=3/(2×3)-2/(2×3)=1/2-1/3
同理
1/(3×4)=1/3-1/4
1/(4×5)=1/4-1/5
1/(5×6)=1/5-1/6
……
1/(98×99)=1/98-1/99
1/(99×100)=1/99-1/100
等号两边同时相加
1/(2×3)+1/(3×4)+1/(4×5)+……+1/(99×100)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/98-1/99+1/99-1/100
=1/2-1/100
=0.5-0.01
=0.49
=49/100为所求
同理
1/(3×4)=1/3-1/4
1/(4×5)=1/4-1/5
1/(5×6)=1/5-1/6
……
1/(98×99)=1/98-1/99
1/(99×100)=1/99-1/100
等号两边同时相加
1/(2×3)+1/(3×4)+1/(4×5)+……+1/(99×100)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/98-1/99+1/99-1/100
=1/2-1/100
=0.5-0.01
=0.49
=49/100为所求
全部回答
- 1楼网友：鱼忧
- 2021-02-05 17:56
你应该是吧分子分母写反了
题目应该是求1/(2×3)+1/(3×4)+1/(4×5)+……+1/(99×100)
我们逐项看
1/(2×3)=(3-2)/(2×3)=3/(2×3)-2/(2×3)=1/2-1/3
同理
1/(3×4)=1/3-1/4
1/(4×5)=1/4-1/5
1/(5×6)=1/5-1/6
……
1/(98×99)=1/98-1/99
1/(99×100)=1/99-1/100
等号两边同时相加
1/(2×3)+1/(3×4)+1/(4×5)+……+1/(99×100)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/98-1/99+1/99-1/100
=1/2-1/100
=0.5-0.01
=0.49
=49/100为所求
题目应该是求1/(2×3)+1/(3×4)+1/(4×5)+……+1/(99×100)
我们逐项看
1/(2×3)=(3-2)/(2×3)=3/(2×3)-2/(2×3)=1/2-1/3
同理
1/(3×4)=1/3-1/4
1/(4×5)=1/4-1/5
1/(5×6)=1/5-1/6
……
1/(98×99)=1/98-1/99
1/(99×100)=1/99-1/100
等号两边同时相加
1/(2×3)+1/(3×4)+1/(4×5)+……+1/(99×100)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/98-1/99+1/99-1/100
=1/2-1/100
=0.5-0.01
=0.49
=49/100为所求
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