PT
2
K
Khách
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PT
4
CX
3 tháng 5 2016
A=3/4.8/9 .15/16.....899/900
A=1.3/2^2 . 2.4 /3^2 . 3.5/4^2 ....... 29.31 / 30^2
A= 1.2.3.....29 / 2.3.4....30 . 3.4.5...31 / 2.3.4....30
A=1/30 . 31/2
A= 31/60
Nhớ k nha
6 tháng 5 2016
A=\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.........\frac{899}{900}\)
A=\(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}..........\frac{29.31}{30.30}\)
A=\(\frac{1.2.3.......29}{2.3.4.......30}.\frac{3.4.5........31}{2.3.4.......30}\)
A=\(\frac{1}{30}.\frac{2}{31}=\frac{1}{465}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
2 tháng 8 2023
C = \(\dfrac{\dfrac{1}{9}-\dfrac{5}{6}-4}{\dfrac{7}{12}-\dfrac{1}{36}-10}\)
C = \(\dfrac{\dfrac{6-45-216}{54}}{\dfrac{21-1-360}{36}}\)
C = \(\dfrac{\dfrac{-85}{18}}{-\dfrac{85}{9}}\)
C = \(\dfrac{1}{2}\)
KN
27 tháng 3 2019
3. \(M=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{10.11.12}\)
\(\Leftrightarrow2M=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{10.11.12}\)
\(\Leftrightarrow2M=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{10.11}-\frac{1}{11.12}\)
\(\Leftrightarrow2M=\frac{1}{1.2}-\frac{1}{11.12}\)
\(\Leftrightarrow2M=\frac{1}{2}-\frac{1}{132}\)
\(\Leftrightarrow2M=\frac{65}{132}\)
\(\Leftrightarrow M=\frac{65}{132}\div2\)
\(\Leftrightarrow M=\frac{65}{264}\)
KN
27 tháng 3 2019
1\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{899}{900}\)
\(\Leftrightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{29.31}{30.30}\)
\(\Leftrightarrow A=\frac{1.3.2.4.3.5...29.31}{2.2.3.3.4.4...30.30}\)
\(\Leftrightarrow A=\frac{\left(1.2.3....29\right)\left(3.4.5...31\right)}{\left(2.3.4...30\right)\left(2.3.4...30\right)}\)
\(\Leftrightarrow A=\frac{1.31}{30.2}\)
\(\Leftrightarrow A=\frac{31}{60}\)
DM
4
7 tháng 6 2015
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.......\frac{899}{900}=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}......\frac{29.31}{30.30}=\frac{1.2.3.....29}{2.3.4......30}.\frac{3.4.5......31}{2.3.4......30}\)
\(=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)
22 tháng 4 2019
\(=\frac{5-\frac{5}{3}-\frac{5}{9}-\frac{5}{27}}{8-\frac{8}{3}-\frac{8}{9}-\frac{8}{27}}:\frac{15-\frac{15}{11}+\frac{15}{121}}{16-\frac{16}{11}+\frac{16}{121}}\)
\(=\frac{5\left(1-\frac{1}{3}-\frac{1}{9}-\frac{1}{27}\right)}{8\left(1-\frac{1}{3}-\frac{1}{9}-\frac{1}{27}\right)}:\frac{15\left(1-\frac{1}{11}+\frac{1}{121}\right)}{16\left(1-\frac{1}{11}+\frac{1}{121}\right)}\)
\(=\frac{5}{8}:\frac{15}{16}=\frac{5}{8}.\frac{16}{15}=\frac{2}{3}\)
\(A=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot....\cdot\frac{960}{961}\)
\(=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}\cdot.....\cdot\frac{30.32}{31.31}\)
\(=\frac{\left(1.2.3....30\right)\left(3.4.5....32\right)}{\left(2.3.4....31\right)\left(2.3.4...31\right)}\)
\(=\frac{32}{31.2}=\frac{32}{62}=\frac{16}{31}\)
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{960}{961}\)
\(\Rightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{30.32}{31.31}\)
\(\Rightarrow A=\frac{1.2.3....30}{2.3.4....31}.\frac{3.4.5.....32}{2.3.4.....31}\)
\(\Rightarrow A=\frac{1}{31}.\frac{32}{2}=\frac{16}{31}\)