hơi lệch

\(1,A=\dfrac{2}{3\cdot7}+\dfrac{2}{7\cdot11}+\dfrac{2}{11\cdot15}+...+\dfrac{2}{99\cdot103}\\ 2A=\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{4}{11\cdot15}+...+\dfrac{4}{99\cdot103}\\ 2A=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{99}-\dfrac{1}{103}\\ 2A=\dfrac{1}{3}-\dfrac{1}{103}=\dfrac{100}{309}\\ A=\dfrac{100}{309}\cdot\dfrac{1}{2}=\dfrac{50}{309}\)

\(2,A=\dfrac{7}{2}+\dfrac{7}{6}+\dfrac{7}{12}+\dfrac{7}{20}+\dfrac{7}{30}+\dfrac{7}{42}+\dfrac{7}{56}+\dfrac{7}{72}+\dfrac{7}{90}\\ A=7\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{9\cdot10}\right)\\ A=7\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ A=7\left(1-\dfrac{1}{10}\right)=7\cdot\dfrac{9}{10}=\dfrac{63}{10}\)

Bài 1: 

Ta có: \(A=\dfrac{2}{3\cdot7}+\dfrac{2}{7\cdot11}+\dfrac{2}{11\cdot15}+...+\dfrac{2}{99\cdot103}\)

\(=\dfrac{1}{2}\left(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{4}{11\cdot15}+...+\dfrac{4}{99\cdot103}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{103}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{100}{309}=\dfrac{50}{309}\)

Bài 2: 

Ta có: \(A=\dfrac{7}{2}+\dfrac{7}{6}+\dfrac{7}{12}+\dfrac{7}{20}+\dfrac{7}{30}+\dfrac{7}{42}+\dfrac{7}{56}+\dfrac{7}{72}+\dfrac{7}{90}\)

\(=7\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}\right)\)

\(=7\left(1-\dfrac{1}{10}\right)\)

\(=\dfrac{63}{10}\)

ta co x :2 : 4 + 505 +579

=> x : 2 : 4 = 579 - 505  = 74

=> x:2 = 74 x 4 = 296

=> x = 296m x 2 

        =  592

x:2:4+505=579

x:2:4=579-505

x:2=74x4

x=296x2

x=592

x:2:4+505=579

x:2:4=579-505

x:2:4=74

x:4=74*4

x:4=296

x=296*4

x=592

Gợi ý: rút gọn cho 101 rồi đặt 5 ra ngoài làm thừa số chung thì sẽ tìm ra kết quả là \(\frac{25}{24}\)

=25/24 đấy

$25/24$ bạn nhé

đáp án:

505 + 495 = 1000

100 . 10 = 1000

chúc bạn học tốt !!!

=1000

=1000

\(505+495=1000\)

\(100\times10=1000\)

_Chúc bạn học tốt_

\(\left(\frac{505}{707}+\frac{222}{333}\right)\cdot x=\frac{404}{909}\)

 =>     \(\left(\frac{5}{7}+\frac{2}{3}\right)\cdot x=\frac{4}{9}\)

=>                     \(\frac{29}{21}\cdot x=\frac{4}{9}\)

=>                               \(x=\frac{4}{9}:\frac{29}{21}\)

=>                              \(x=\frac{28}{87}\)

TK mk nha!

( 505/707+ 222/333) . x = 404/ 909

29/21 . x = 4/9

x= 4/9 : 29/21

x= 4/9 . 21/29

x= 28/87

Vậy x= 28/87

28/87

Ta có : 16<17 => 16⁵⁰⁵<17⁵⁰⁵

                       => (2⁴)⁵⁰⁵<17⁵⁰⁵

                       => 2²⁰²⁰<17⁵⁰⁵

Mà 2²⁰¹⁸<2²⁰²⁰ 

=> 2²⁰¹⁸<17⁵⁰⁵

Vậy 2²⁰¹⁸<17⁵⁰⁵.

Ta có :\(\frac{230+x}{505+x}=\frac{4}{5}\)

\(\Rightarrow5.\left(230+x\right)=4.\left(505+x\right)\)

\(\Rightarrow1150+5x=2020+4x\)

\(\Rightarrow5x-4x=2020-1150\)

\(\Rightarrow x=870\)

Vậy x =870

X=870

X=870 đó bạn