a) \(\frac{1212}{1515}\):\(\frac{2727}{2525}\)

=   \(\frac{1212}{1515}\)* \(\frac{2525}{2727}\)

=     \(\frac{101.12}{101.15}\)* \(\frac{101.25}{101.27}\)

=      \(\frac{12}{15}\). \(\frac{25}{27}\)

=       \(\frac{20}{27}\)

b) ban co the viet ro hon de bai dc ko?

\(\frac{1010+1111+1212+1313+1414+1515+1616+1717}{2020+2121+2222+2323+2424+2525+2626+2727}\)

\(=\frac{101.10+101.11+...+101.17}{101.20+101.21+...+101.27}\)

\(=\frac{101.\left(10+11+...+17\right)}{101.\left(20+21+...+27\right)}\)

\(=\frac{108}{188}\)

\(=\frac{27}{47}\)

\(2>\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}\right)\cdot5.y>\frac{5}{6}\)

\(\Rightarrow2>\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{1}{24}\right):5.y>\frac{5}{6}\)

\(\Rightarrow2>\left(\frac{20}{120}+\frac{16}{120}+\frac{9}{120}+\frac{5}{120}\right):5.y>\frac{5}{6}\)

\(\Rightarrow2>\frac{5}{12}:5.y>\frac{5}{6}\)

\(\Rightarrow2>\frac{1}{12}.y>\frac{5}{6}\)

Đặt :\(\frac{1}{12}.y=2\Rightarrow y=2:\frac{1}{12}=24\)

\(\frac{1}{12}.y=\frac{5}{6}\Rightarrow y=\frac{5}{6}:\frac{1}{12}=10\)

\(\Rightarrow24>y>10\)

\(\Rightarrow y\in\left\{11;12;...;23\right\}\)

ko biết

I am sorry

Kb nhé

Toan lop 5 ha ma

rút gọn

\(1,\frac{1212}{1515}+\frac{1212}{3535}+\frac{1212}{6363}+\frac{1212}{9999}=\frac{12}{15}+\frac{12}{35}+\frac{12}{63}+\frac{12}{99}=6\left(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\right)=6\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right).Tacocongthuc:\frac{1}{n}-\frac{1}{n+k}=\frac{k}{n\left(n+k\right)}\Rightarrow\frac{1212}{1515}+\frac{1212}{3535}+\frac{1212}{6363}+\frac{1212}{9999}=6\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-.....-\frac{1}{11}\right)=6\left(\frac{1}{3}-\frac{1}{11}\right)=\frac{48}{33}=\frac{16}{11}\)

\(2,\left(x+1\right)+\left(x+2\right)+.....+\left(x+211\right)=211x+\left(1+2+....+211\right)=211x+\frac{212.211}{2}=211x+22366=23632\Leftrightarrow211x=23632-22366=1266\Leftrightarrow x=6\)

a, \(14:\left(4\frac{2}{3}:1\frac{5}{9}\right)+14:\left(\frac{2}{3}+\frac{8}{9}\right)\)

=> \(14:\frac{28}{9}+14:\frac{14}{9}=>14.\frac{9}{28}+14.\frac{9}{14}\)

=> 14. ( \(\frac{9}{28}+\frac{9}{14}\) )

=> \(14.\frac{27}{28}=\frac{419}{28}\)

b, \(\frac{1212}{1515}+\frac{1212}{3535}+\frac{1212}{6363}+\frac{1212}{9999}\)

=> \(\frac{4}{5}+\frac{12}{35}+\frac{4}{21}+\frac{4}{33}\)

=> \(\frac{8}{7}+\frac{24}{77}=\frac{16}{11}\)

bài 2 :

( x + 1 ) + ( x + 2 ) + ... + ( x + 211 ) = 23632

=> ( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 211 ) = 23632

=> 211x + 22366 = 23632

=> 211x = 23632 - 22366

=> 211x = 1266

=> x = 1266 : 211

x = 6

\(\left(x+\frac{3}{4}\right)\times\frac{5}{7}=\frac{10}{9}\)

\(\Rightarrow x+\frac{3}{4}=\frac{10}{9}:\frac{5}{7}=\frac{10}{9}\times\frac{7}{5}=\frac{14}{9}\)

\(\Rightarrow x=\frac{14}{9}-\frac{3}{4}=\frac{56-27}{36}=\frac{29}{36}\)

\(\left(x+\frac{3}{4}\right)\times\frac{5}{7}=\frac{10}{9}\)

\(\Leftrightarrow x+\frac{3}{4}=\frac{14}{9}\)

\(\Rightarrow x=\frac{29}{36}\)

P/s tham khảo nha

\(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}.\text{ CMR : }\frac{7}{12}< A< \frac{5}{6}\)

Ta có :

\(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{99.100}\)

\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\)

\(A=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{99}+\frac{1}{100}-2.\frac{1}{2}-2.\frac{1}{4}-...-2.\frac{1}{98}\)

\(A=1+...+\frac{1}{100}-1-\frac{1}{2}-\frac{1}{3}-...-\frac{1}{49}\)

\(A=\frac{1}{51}+...+\frac{1}{100}\)

\(\Rightarrow A< \frac{1}{51.25}=\frac{25}{51}< \frac{25}{30}=\frac{5}{6}\) (đpcm)

Và \(A>25.\frac{1}{75}+25.\frac{1}{100}=\frac{7}{12}\)

Ta có : A = 1 / (1.2) + 1 / (3.4) + ... + 1 / (99.100) > 1 / (1.2) + 1 / (3.4) = 1 / 2 + 1 / 12 = 7 / 12 (1)

Lại có : A = 1 / (1.2) + 1 / (3.4) + ... + 1 / (99.100) = (1 - 1 / 2) + (1 / 3 - 1 / 4) + ... + (1 / 99 - 100)

                =  (1 - 1 / 2 + 1 / 3) - (1 / 4 - 1 / 5) - (1 / 6 - 1 / 7) - ... - (1 / 98 - 1 / 99) - 1 / 100 <  1 - 1 / 2 + 1 / 3 = 5 / 6 (2)

Từ (1) và (2) => 7 / 12 < A < 5 / 6

trả lời :

Ta có : A = 1 / (1.2) + 1 / (3.4) + ... + 1 / (99.100) > 1 / (1.2) + 1 / (3.4) = 1 / 2 + 1 / 12 = 7 / 12 (1)

Lại có : A = 1 / (1.2) + 1 / (3.4) + ... + 1 / (99.100) = (1 - 1 / 2) + (1 / 3 - 1 / 4) + ... + (1 / 99 - 100)

                =  (1 - 1 / 2 + 1 / 3) - (1 / 4 - 1 / 5) - (1 / 6 - 1 / 7) - ... - (1 / 98 - 1 / 99) - 1 / 100 <  1 - 1 / 2 + 1 / 3 = 5 / 6 (2)

Từ (1) và (2) => 7 / 12 < A < 5 / 6

^HT^

1 

Ez lắm =)

Bài 1:

Với mọi gt \(x,y\in Q\) ta luôn có: 

\(x\le\left|x\right|\) và \(-x\le\left|x\right|\) 

\(y\le\left|y\right|\) và \(-y\le\left|y\right|\Rightarrow x+y\le\left|x\right|+\left|y\right|\) và \(-x-y\le\left|x\right|+\left|y\right|\)

Hay: \(x+y\ge-\left(\left|x\right|+\left|y\right|\right)\)

Do đó: \(-\left(\left|x\right|+\left|y\right|\right)\le x+y\le\left|x\right|+\left|y\right|\)

Vậy: \(\left|x+y\right|\le\left|x\right|+\left|y\right|\)

Dấu "=" xảy ra khi: \(xy\ge0\)

Bài 3: 

Ta có: \(\frac{x}{a}=\frac{y}{b}=\frac{z}{c}=\frac{x+y+z}{a+b+c}=x+y+z\) (vì a + b + c = 1)

Do đó: \(\left(x+y+z\right)^2=\frac{x^2}{a^2}=\frac{y^2}{b^2}=\frac{z^2}{c^2}=\frac{x^2+y^2+z^2}{a^2+b^2+c^2}=x^2+y^2+z^2\) (vì a² + b² + c² = 1)

Vậy: (x + y + z)² = x² + y² + z²

\(=\frac{6}{5}\times\frac{7}{6}\times...\times\frac{11}{10}\)(lại lỗi đề)

\(=\frac{6×7×...×11}{5×6×...×10}\)

\(=\frac{11}{5}\)

\(1\frac{1}{5}\cdot1\frac{1}{6}\cdot1\frac{1}{7}\cdot1\frac{1}{8}\cdot1\frac{1}{9}\cdot1\frac{1}{10}\)

\(=\frac{6}{5}\cdot\frac{7}{6}\cdot\frac{8}{7}\cdot\frac{9}{8}\cdot\frac{10}{9}\cdot\frac{11}{10}\)

\(=\frac{6\cdot7\cdot8\cdot9\cdot10\cdot11}{5\cdot6\cdot7\cdot8\cdot9\cdot10}\)

\(=\frac{11}{5}\)

ta có:

                  \(\left(7\frac{1}{2}.8\frac{3}{70}+8\frac{3}{70}.\frac{9}{4}+\frac{19}{4}.8\frac{3}{70}+5\frac{1}{2}.8\frac{3}{70}\right):x=1126\)

                                                  \(8\frac{3}{70}\left(7\frac{1}{2}+\frac{9}{4}+\frac{19}{4}+5\frac{1}{2}\right):x=1126\)

                                                                \(\frac{563}{70}.\left(\frac{15}{2}+7+\frac{11}{2}\right):x=1126\)

                                                                                             \(\frac{563}{70}.20:x=1126\)

                                                                                                 \(\frac{1126}{70}:x=1126\)

                                                                                                   \(=>x=\frac{1126}{7}:1126\)

                                                                                                    \(=>x=\frac{1}{7}\)

            cho mình nha các bạn.

cho mình nha.