A = 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/100^2

1/2^2 < 1/1*2

1/3^2 < 1/2*3

1/4^2 < 1/3*4

...

1/100^2 < 1/99*100

=> A < 1/1*2 + 1/2*3 + 1/3*4 + ... + 1/99*100

=> A < 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100

=> A < 1 - 1/100

=> A < 1

minh deo can ban k dau :((

\(a,\frac{1}{2}x+\frac{3}{5}(x-2)=3\)

\(\Rightarrow\frac{1}{2}x+\frac{3}{5}x-\frac{6}{5}=3\)

\(\Rightarrow\left[\frac{1}{2}+\frac{3}{5}\right]x=3+\frac{6}{5}\)

\(\Rightarrow\left[\frac{5}{10}+\frac{6}{10}\right]x=\frac{21}{5}\)

\(\Rightarrow\frac{11}{10}x=\frac{21}{5}\)

\(\Rightarrow x=\frac{21}{5}:\frac{11}{10}=\frac{21}{5}\cdot\frac{10}{11}=\frac{21}{1}\cdot\frac{2}{11}=\frac{42}{11}\)

Vậy x = 42/11

\(A=\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

\(A=\frac{1}{10.9}-\frac{1}{9.8}-\frac{1}{8.7}-\frac{1}{7.6}-\frac{1}{6.5}-\frac{1}{5.4}-\frac{1}{4.3}-\frac{1}{3.2}-\frac{1}{2.1}\)

\(-A=\left(\frac{1}{10.9}+\frac{1}{9.8}+\frac{1}{8.7}+\frac{1}{7.6}+...+\frac{1}{3.2}+\frac{1}{2.1}\right)\)

\(-A=\frac{1}{10}-\frac{1}{9}+\frac{1}{9}-\frac{1}{8}+\frac{1}{8}-\frac{1}{7}+...+\frac{1}{3}-\frac{1}{2}+\frac{1}{2}-1\)

\(-A=\frac{1}{10}-1=\frac{-9}{10}\Rightarrow A=\frac{9}{10}\)

\(A=\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

\(=\frac{1}{90}-\left(\frac{1}{72}+\frac{1}{56}+\frac{1}{42}+\frac{1}{30}+\frac{1}{20}+\frac{1}{12}+\frac{1}{6}+\frac{1}{2}\right)\)

\(=\frac{1}{90}-\left(\frac{1}{8.9}+\frac{1}{7.8}+\frac{1}{6.7}+\frac{1}{5.6}+\frac{1}{4.5}+\frac{1}{3.4}+\frac{1}{2.3}+\frac{1}{1.2}\right)\)

\(=\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)

\(=\frac{1}{90}-\left(1-\frac{1}{9}\right)=\frac{1}{90}-\frac{8}{9}=-\frac{79}{90}\)

Vậy A=-79/90

A=1/1.2-1/2.3-1/3.4-1/4.5-1/5.6-1/6.7-1/7.8-1/8.9-1/9.10(mình làm ngược lại nha)

A=1/1-1/2-1/2-1/3-1/3-1/4-1/4-1/5-1/5-1/6-1/6-1/7-1/7-1/8-1/8-1/9

A=1/1-1/9

A=8/9

\(\frac{\left[\left(6\frac{3}{5}-3\frac{3}{14}\right)\cdot5\frac{5}{6}\right]}{\left(21-1,25\right):2,5}\)

Đặt 2 biểu thức trên là A và B

Ta có : \(A=\left[\left(6\frac{3}{5}-3\frac{3}{14}\right)\cdot5\frac{5}{6}\right]\)

\(A=\left[\left(\frac{33}{5}-\frac{45}{14}\right)\cdot\frac{35}{6}\right]\)

\(A=\left[\frac{237}{70}\cdot\frac{35}{6}\right]=\frac{79}{4}\)

Vậy A = 79/4

\(B=\left[\left(21-1,25\right):2,5\right]\)

\(B=\left[\left(21-\frac{5}{4}\right):\frac{5}{2}\right]\)

\(B=\frac{79}{4}:\frac{5}{2}=\frac{79}{4}\cdot\frac{2}{5}=\frac{79}{10}\)

Vậy B = 79/10

Do đó \(\frac{A}{B}=\frac{\frac{79}{4}}{\frac{79}{10}}=\frac{79}{4}\cdot\frac{10}{79}=\frac{10}{4}=\frac{5}{2}\)

mk cảm ơn bn nhìu

[(33/5-45/14.)35/6]:[(21-1,25):2,5]

[237/70.35/6]:[(21-1/25):2,5]

79/4:[(21-1,25):2,5]

79/4:[19,75:2,5]

79/4:79/10

79/4.10/79

5/2

\(a,\frac{x+5}{20}=-\frac{5}{4}\)

\(\left(x+5\right):20=\frac{-5}{4}\)

\(x+5=-\frac{5}{4}\times20\)

\(x+5=-25\)

        \(x=-25-5\)

        \(x=-30\)

các câu khác thì theo đó tự làm nha

bn ơi các câu a, b thì mk làm đc nhưng vướng câu c đó bn ạ

\(\frac{4}{3}.\left(\frac{1}{6}-\frac{1}{2}\right)\le x\le\frac{2}{3}.\left(\frac{-1}{6}+\frac{3}{4}\right)\)

\(\frac{4}{3}.\frac{-1}{3}\le x\le\frac{2}{3}.\frac{7}{12}\)

\(\frac{-4}{9}\le x\le\frac{7}{18}\)

\(\frac{-8}{18}\le x\le\frac{7}{18}\)

\(\Rightarrow\)X \(\in\) {\(\frac{-7}{18};\frac{-6}{18};\frac{-5}{18};\frac{-4}{18};\frac{-3}{18};\frac{-2}{18};\frac{-1}{18};0;\frac{1}{18};\frac{2}{18};\frac{3}{18};\frac{4}{18};\frac{5}{18};\frac{6}{18}\)}

 o0oNguyễno0o bn giúp mk nha bài này khó wa

 Harry Potter05 giúp mk đc ko vậy bn!!!

 o0oNguyễno0o giúp mk nhanh ik nha

Nhân vô rồi chuyển dấu lên và nhóm nhân -1ra ngoài rồi trg ngoặc là dãy có quy luật giải dãy đó r nhân phá ngoặc

A = 1/ 1² +1/2²+1/3²+. . . +1/50² < 1+ 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5+ . . . + 1/49.50

<=> A < 1 + 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +. . . + 1/49 - 1/50

<=> A< 1 + 1 - 1/50 = 2 - 1/50 

Vậy A < 2

Nhớ k nhé bạn ^^