hỏi chị google ấy

A= \(\frac{1}{31}.\left[\frac{5}{31}\left(9-\frac{1}{2}\right)-\frac{17}{2}\left(4+\frac{1}{5}\right)\right]+\frac{1}{2}+\frac{1}{6}+...+\frac{1}{930}\)

= \(\frac{1}{31}.\left(\frac{5}{31}.\frac{17}{2}-\frac{17}{2}.\frac{21}{5}\right)+\frac{1}{2}+\frac{1}{6}+...+\frac{1}{930}\)

=\(\frac{1}{31}.\left[\frac{17}{2}.\left(\frac{5}{31}-\frac{21}{5}\right)\right]+\frac{1}{2}+\frac{1}{6}+...+\frac{1}{930}\)

=\(\frac{1}{31}.\left[\frac{17}{2}.\left(\frac{-626}{155}\right)\right]+\frac{1}{2}+\frac{1}{6}+...+\frac{1}{930}\)

=\(\frac{1}{31}.\left(\frac{-5321}{155}\right)+\frac{1}{2}+\frac{1}{6}+...+\frac{1}{930}\)

=\(\frac{-5321}{4805}+\frac{1}{2}+\frac{1}{6}+...+\frac{1}{930}\)

=\(\frac{-5321}{4805}+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{30.31}\)

=\(\frac{-5321}{4805}+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{30}-\frac{1}{31}\)

=\(\frac{-5321}{4805}+\frac{1}{1}-\frac{1}{31}\)

=\(\frac{-5321}{4805}+\frac{30}{31}\)

=\(\frac{-671}{4805}\)

lamf như thế nào

\(\Rightarrow5H=\frac{1}{5}+\frac{2}{5^2}+...+\frac{11}{5^{11}}\)

\(\Rightarrow5H-H=\left(\frac{1}{5}+\frac{2}{5^2}+...+\frac{11}{5^{11}}\right)-\left(\frac{1}{5^2}+\frac{2}{5^3}+...+\frac{11}{5^{12}}\right)\)

\(\Rightarrow4H=\frac{1}{5}+\frac{1}{5^2}+..+\frac{1}{5^{11}}-\frac{11}{5^{12}}\)

Đặt \(A=\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{11}}\)

\(\Rightarrow5A=1+\frac{1}{5}+...+\frac{1}{5^{10}}\)

\(\Rightarrow5A-A=\left(1+..+\frac{1}{5^{10}}\right)-\left(\frac{1}{5}+...+\frac{1}{5^{11}}\right)\)

\(\Rightarrow4A=1-\frac{1}{5^{11}}\)

\(\Rightarrow A=\frac{1}{4}-\frac{1}{4.5^{11}}\)

\(\Rightarrow4H=\frac{1}{4}-\frac{1}{4.5^{11}}-\frac{11}{5^{12}}\)

\(\Rightarrow H=\frac{1}{16}-\frac{1}{4^2.5^{11}}-\frac{11}{4.5^{12}}\)

Ta có : \(5H=\frac{1}{5}+\frac{2}{5^2}+...+\frac{11}{5^{11}}\)

\(\Rightarrow4H=\left(\frac{1}{5}+\frac{2}{5^2}+...+\frac{11}{5^{11}}\right)-\left(\frac{1}{5^2}+\frac{2}{5^3}+...+\frac{11}{5^{12}}\right)=\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{11}}+\frac{11}{5^{12}}\)

\(\Rightarrow20H=1+\frac{1}{5}+...+\frac{1}{5^{10}}+\frac{11}{5^{11}}\)

\(\Rightarrow16H=20H-4H=1+\frac{10}{5^{11}}-\frac{11}{5^{12}}\Leftrightarrow H=\frac{1+\frac{10}{5^{11}}-\frac{11}{5^{12}}}{16}.\)

Bài 2

a, \(\dfrac{4}{5}+\dfrac{2}{7}-\dfrac{7}{10}=\) \(\dfrac{27}{70}\)

giải thik từng bước đi bạn

*) So sánh \(\frac{-4}{5}\) và -1

Ta có : -1 = \(\frac{-5}{5}\)

mà \(\frac{-5}{5}\) < \(\frac{-4}{5}\) ( do -5 < -4 )

=> -1 < \(\frac{-4}{5}\)

*) So sánh \(\frac{3}{4}\) và \(\frac{4}{5}\)

Ta có : \(\frac{3}{4}+\frac{1}{4}=1\)

=> \(\frac{3}{4}=1-\frac{1}{4}\) (1)

\(\frac{4}{5}+\frac{1}{5}=1\)

=> \(\frac{4}{5}=1-\frac{1}{5}\) (2)

Do \(\frac{1}{4}>\frac{1}{5}\) ( vì 4 < 5 )

=> 1 - \(\frac{1}{4}\) < 1 - \(\frac{1}{5}\) (3)

Từ (1),(2),(3) ta có : \(\frac{3}{4}< \frac{4}{5}\)

Ta có : -4/5 < -1

và -1= -1

=> -4/5<-1 Vậy -4/5< -1

Ta có : 3/4 = 15/20

và 4/5 = 16/20

Mà 15< 16 => 15/20 < 16 / 20

=>3/4< 4/5

Vậy 3/4 < 4/5