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13 tháng 8 2015
1/3+1/6+1/10+1/15+......+1/4950
=2x（1/6+1/12+1/20+1/30+……+1/9900）
=2x（1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/99-1/100）
=2x（1/2-1/100）
=1-1/50
=49/50
**** nhé
HS
1
LL
1
IA
8 tháng 3 2020
\(\frac{1\cdot3\cdot9+2\cdot6\cdot18+3\cdot9\cdot27}{1\cdot5\cdot18+2\cdot10\cdot36+3\cdot15\cdot54}\)
\(=\frac{1\cdot3\cdot9+2\left(1\cdot3\cdot9\right)+3\left(1\cdot3\cdot9\right)}{1\cdot5\cdot18+2\left(1\cdot5\cdot18\right)+3\left(1\cdot5\cdot18\right)}\)
\(=\frac{\left(1\cdot3\cdot9\right)\left(1+2+3\right)}{\left(1\cdot5\cdot18\right)\left(1+2+3\right)}\)
\(=\frac{3}{10}\)
LM
Lê Minh Vũ
VIP
15 tháng 6 2023
3 x 15 + 21 x 15 + 85 x 5
= 45 + 315 + 425
= 785
15 - 30 + 40
= 25
21 + 19 - 50 + 10
= 0
\(\dfrac{1}{5}-\dfrac{1}{4}+2\)
\(=-\dfrac{1}{20}+2\)
\(=\dfrac{39}{20}\)
\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)
\(=\dfrac{5}{12}\times\dfrac{1}{4}\)
\(=\dfrac{5}{12}\times\dfrac{3}{12}\)
\(=\dfrac{5}{48}\)
\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)
\(=-\dfrac{9}{20}\)
BD
15 tháng 6 2023
\(3\times15+21\times15+85\times5\\ =15\times\left(3+21\right)+425\\ =15\times24+425\\ =360+425\\ =785\)
\(15-30+40\\ =\left(15+40\right)-30\\ =55-30\\ =25\)
\(21+19-50+10\\ =\left(21+19\right)-\left(50-10\right)\\ =40-40\\ =0\)
\(\dfrac{1}{5}-\dfrac{1}{4}+2\)
\(=\dfrac{4}{20}-\dfrac{5}{20}+\dfrac{40}{20}\)
\(=\dfrac{\left(4+40\right)}{20}-\dfrac{5}{20}\)
\(=\dfrac{44}{20}-\dfrac{5}{20}\)
\(=\dfrac{39}{20}\)
\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)
\(=\dfrac{5}{12}\times\dfrac{1}{4}\)
\(=\dfrac{5}{48}\)
\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)
\(=\dfrac{2}{20}+\dfrac{4}{20}-\dfrac{15}{20}\)
\(=\dfrac{6}{20}-\dfrac{15}{20}\)
\(=-\dfrac{9}{20}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
19 tháng 8 2023
A , 34 - \(\dfrac{x}{30}\) = \(\dfrac{5}{6}\)
\(\dfrac{x}{30}\) = 34 - \(\dfrac{5}{6}\)
\(\dfrac{x}{30}=\) \(\dfrac{199}{6}\)
\(\dfrac{x}{30}=\) \(\dfrac{995}{30}\)
x = 995
B x +\(\dfrac{13}{34}\) = \(\dfrac{12}{17}\)
x = \(\dfrac{12}{17}-\dfrac{13}{34}\)
x = \(\dfrac{11}{34}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
19 tháng 8 2023
\(\dfrac{7}{9}=\dfrac{21}{27};\dfrac{7}{10}=\dfrac{21}{30}\)
hai số nằm giữa \(\dfrac{7}{9}\) và \(\dfrac{7}{10}\)
\(\dfrac{21}{27}>\dfrac{21}{28}>\dfrac{21}{29}>\dfrac{21}{30}\)
ND
0
Đặt \(A=\dfrac{2}{3}+\dfrac{2}{6}+...+\dfrac{2}{4950}\)
\(\dfrac{1}{2}\times A=\dfrac{2}{2\times3}+\dfrac{2}{2\times6}+...+\dfrac{2}{2\times4950}\)
\(\dfrac{1}{2}\times A=\dfrac{2}{2\times3}+\dfrac{2}{3\times4}+...+\dfrac{2}{99\times100}\)
\(\dfrac{1}{2}\times A=2\times\left(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+...+\dfrac{1}{99\times100}\right)\)
\(\dfrac{1}{2}\times A=2\times\left(\dfrac{3-2}{2\times3}+\dfrac{4-3}{3\times4}+...+\dfrac{100-99}{99\times100}\right)\)
\(\dfrac{1}{4}\times A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(\dfrac{1}{4}\times A=\dfrac{1}{2}-\dfrac{1}{100}\)
\(\dfrac{1}{4}\times A=\dfrac{49}{100}\)
\(A=\dfrac{49}{100}:\dfrac{1}{4}=\dfrac{49}{25}\)