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7 tháng 11 2020

\(\left(\frac{2}{5}+\frac{2}{7}+\frac{2}{11}\right)\div\left(\frac{3}{5}+\frac{3}{7}+\frac{3}{11}\right)\)

\(=2\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{11}\right)\div3\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{11}\right)\)

\(=\frac{2\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{11}\right)}{3\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{11}\right)}\)

\(=\frac{2}{3}\)

b: \(27D=3^{14}+3^{17}+...+3^{2024}\)

\(\Leftrightarrow26D=3^{2024}-3^{11}\)

hay \(D=\dfrac{3^{2024}-3^{11}}{26}\)

c: \(25E=-5^4-5^6-...-5^{1002}\)

\(\Leftrightarrow24E=-5^{1002}+5^2\)

hay \(E=\dfrac{-5^{1002}+5^2}{24}\)

16 tháng 1 2022

sai nha

 

6 tháng 7 2018

A=3.(1/1.2+1/2.3+1/3.4+.....+1/399.400)

A=3.(1/1-1/2+1/2-1/3+......+1/399-1/400)

A=3.(1-1/400)

A=3.399/400

A=1197/400

6 tháng 7 2018

A=3.(1/1.2+1/2.3+1/3.4+.....+1/399.400)

A=3.(1/1-1/2+1/2-1/3+......+1/399-1/400)

A=3.(1-1/400)

A=3.399/400

A=1197/400

5 tháng 7 2018

Bài 1: Tính nhanh:

A = 3/1*2 + 3/2*3 + 3/3*4 + ... + 3/399*400

=>3A = 1/1*2 + 1/2*3 + 1/3*4 + ... + 1/399*400

    3A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/399 - 1/400

    3A = 1 - 1/400

      3A = 400/400 - 1/400

      3A = 399/400

        A = 399/400 : 3

        A = 399/400 . 1/3

        A = 133/400.

Có gì ko hiểu bn ib mk nha.^^

5 tháng 7 2018

\(A=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{399.400}\)

\(A=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{399.400}\right)\)

\(A=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{399}-\frac{1}{400}\right)\)

\(A=3.\left(1-\frac{1}{400}\right)\)

\(A=3.\frac{399}{400}\)

\(A=\frac{1197}{400}\)

\(B=\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+...+\frac{5}{399.400}\)

\(B=5.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{399.400}\right)\)

\(B=5.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{399}-\frac{1}{400}\right)\)

\(B=5.\left(1-\frac{1}{400}\right)\)

\(B=5.\frac{399}{400}\)

\(B=\frac{399}{80}\)

\(C=\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{149.151}\)

\(C=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{149}-\frac{1}{151}\)

\(C=\frac{1}{5}-\frac{1}{151}\)

\(C=\frac{146}{755}\)

\(D=\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+...+\frac{3}{149.151}\)

\(D=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{149.151}\right)\)

\(D=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{149}-\frac{1}{151}\right)\)

\(D=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{151}\right)\)

\(D=\frac{3}{2}.\frac{146}{755}\)

\(D=\frac{219}{755}\)

\(E=\frac{11}{1.3}+\frac{11}{3.5}+\frac{11}{5.7}+...+\frac{11}{99.101}\)

\(E=\frac{11}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

\(E=\frac{11}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(E=\frac{11}{2}.\left(1-\frac{1}{101}\right)\)

\(E=\frac{11}{2}.\frac{100}{101}\)

\(E=\frac{550}{101}\)

_Chúc bạn học tốt_

23 tháng 4 2018

a ,b

cách 1 : cộng 2 số trong ngặc rồi tính bình thường 

cách 2 : nhân phân phối ra rồi tính nhân chia trước cộng trừ sau

c,d

cách 1 : tính bình thường, nhân chia trc cộng trừ sau

cách 2 : đặt nhân tử ( thừa số ) chung

23 tháng 4 2018

Cách 1 : \((\frac{6}{11}+\frac{5}{11})\cdot\frac{3}{7}=1\cdot\frac{3}{7}=\frac{3}{7}\)

Cách 2 : \(\frac{6}{11}\cdot\frac{3}{7}+\frac{5}{11}\cdot\frac{3}{7}=\frac{18}{77}+\frac{15}{77}=\frac{33}{77}=\frac{3}{7}\)

Cách 1 dễ rồi nha

Cách 2 : \(\frac{6}{7}:\frac{2}{5}-\frac{4}{7}:\frac{2}{5}=\frac{15}{7}-\frac{10}{7}=\frac{5}{7}\)

Cách 1 tự làm

Cách 2 : \(\frac{3}{5}\cdot(\frac{7}{9}-\frac{2}{9})=\frac{3}{5}\cdot\frac{5}{9}=\frac{1}{3}\)

Cách 1 : ...

Cách 2 : \((\frac{8}{15}+\frac{7}{15}):\frac{2}{11}=1:\frac{2}{11}=\frac{2}{11\cdot1}=\frac{2}{11}\)

`@` `\text {Ans}`

`\downarrow`

`a)`

\(\dfrac{3}{4}+\dfrac{2}{3}+\dfrac{3}{5}\)

`=`\(\dfrac{9}{12}+\dfrac{8}{12}+\dfrac{3}{5}\)

`=`\(\dfrac{17}{12}+\dfrac{3}{5}\)

`=`\(\dfrac{85}{60}+\dfrac{36}{60}\)

`=`\(\dfrac{121}{60}\)

`b)`

\(\dfrac{1}{2}\cdot\dfrac{9}{13}\div\dfrac{27}{26}\)

`=`\(\dfrac{1}{2}\cdot\dfrac{9}{13}\cdot\dfrac{26}{27}\)

`=`\(\dfrac{1}{2}\cdot\dfrac{2}{3}\)

`=`\(\dfrac{1}{3}\)

`c)`

\(\dfrac{2}{7}\cdot\dfrac{1}{9}+\dfrac{2}{7}\cdot\dfrac{2}{9}+\dfrac{1}{3}\cdot\dfrac{5}{7}\)

`=`\(\dfrac{2}{7}\cdot\left(\dfrac{1}{9}+\dfrac{2}{9}\right)+\dfrac{1}{3}\cdot\dfrac{5}{7}\)

`=`\(\dfrac{2}{7}\cdot\dfrac{1}{3}+\dfrac{1}{3}\cdot\dfrac{5}{7}\)

`=`\(\dfrac{1}{3}\cdot\left(\dfrac{2}{7}+\dfrac{5}{7}\right)\)

`=`\(\dfrac{1}{3}\cdot1=\dfrac{1}{3}\)

`d)`

\(11\div\dfrac{5}{2}+11\div\dfrac{7}{3}+11\div\dfrac{35}{6}\)

`=`\(11\cdot\dfrac{2}{5}+11\cdot\dfrac{3}{7}+11\cdot\dfrac{6}{35}\)

`=`\(11\cdot\left(\dfrac{2}{5}+\dfrac{3}{7}+\dfrac{6}{35}\right)\)

`=`\(11\cdot1=11\)

19 tháng 7 2023

a) 3/4 + 2/3 + 3/5 = 45/60 + 40/60 + 36/60 = 121/60

b) 1/2 x 9/13 : 27/26 = 9/26 x 26/27 = 1/3

c) 2/7 x 1/9 + 2/7 x 2/9 + 1/3 x 5/7 = 2/7 x (1/9 + 2/9) + 5/21 = 2/7 x 1/3 + 5/21 = 2/21 + 5/21 = 1/3

d) 11 : 5/2 + 11 : 7:3 + 11 : 35/6 = 11 x (2/5 + 3/7 + 6/35) = 11 x 1 = 11 

13 tháng 5 2017

d)\(\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{97.99}\) 

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{97}-\frac{1}{99}\)

\(=\frac{1}{3}-\frac{1}{99}\)

\(=\frac{32}{99}\)

13 tháng 5 2017

a)   11/4x(-0,4)x-1,6x11/4

     = -1,1 x-1,6x11/4

    = 1,76x11/4

    = 4,48

b)    6/19x-7/11+6/19x-4/19x-4/11+13/19

     = -42/209+96/3971+13/19

     = -702/3971+13/19

     = 2015/3971

c)     2/5x3/7+-3/7x3/5+3/7

      = 3/7x(2/5+3/5+1)

      = 3/7x(1+1)

      = 3/7x2

      = 6/7

d)      2/3x5+2x5/7+2/7x9+....+2/97x99

      = 1/3-1/5+1/5-1/7+1/7-1/9+......+1/97-1/99

      = 1/3-1/99

      = 32/99

26 tháng 3 2022

A.3/7

B.3/5

C.5/7

D.11/2

k hộ mình nha!

11 tháng 8 2016

a)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{3}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(1+\left(\frac{-1}{2}+\frac{1}{2}\right)+\left(\frac{-1}{3}+\frac{1}{3}\right)+...+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{10}\)

\(1-\frac{1}{10}\)

=\(\frac{9}{10}\)

b)\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)

\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

=\(1+\left(\frac{-1}{3}+\frac{1}{3}\right)+\left(\frac{-1}{5}+\frac{1}{5}\right)+\left(\frac{-1}{7}+\frac{1}{7}\right)+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{11}\)

=\(1-\frac{1}{11}\)

\(\frac{10}{11}\)

c) đặt A=\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}\)

     \(\frac{1}{3}A\)=\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)

     \(\frac{2}{3}A\)=\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)

      \(\frac{2}{3}A\)=\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

     \(\frac{2}{3}A\)=\(1+\left(\frac{-1}{3}+\frac{1}{3}\right)+\left(\frac{-1}{5}+\frac{1}{5}\right)+\left(\frac{-1}{7}+\frac{1}{7}\right)+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{11}\)

     \(\frac{2}{3}A\)=\(\frac{10}{11}\)

         A= \(\frac{10}{11}:\frac{2}{3}\)

          A= \(\frac{10}{11}.\frac{3}{2}\)=\(\frac{15}{11}\)

d) giả tương tự câu c kết quả \(\frac{25}{11}\)

11 tháng 8 2016

tổng đặc biệt đó bạn

\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{9\times10}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

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

những câu sau cũng áp dụng như vậy nhé

19 tháng 3 2017

B=4*13/9*3-4/3*40/9

B=4/3*13/9-4/3*40/9

B=4/3*(13/9-40/9)

B=4/3*(-27)/9

B=4*(-3)/9

B=-4

19 tháng 3 2017

A=6/7 + 1/7.(2/7+5/7)

A=6/7 + 1/7.7/7=6/7+1/7.1

A=6/7+1/7=7/7=1