\(1+\frac{7}{1\cdot2}+\frac{7}{2\cdot3}+\frac{7}{3\cdot4}+...+\frac{7}{59\cdot60}\)

\(=1+7\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{59\cdot60}\right)\)

\(=1+7\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{59}-\frac{1}{60}\right)\)

\(=1+7\left(1-\frac{1}{60}\right)\)

\(=1+7\cdot\frac{59}{60}\)

Cảm ơn bạn nha Sooya.

\(A=\dfrac{7}{1.2}+\dfrac{7}{2.3}+\dfrac{7}{3.4}+...+\dfrac{7}{2011.2012}\)

\(A=7\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2011.2012}\right)\)

\(A=7\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2011}-\dfrac{1}{2012}\right)\)

\(A=7\left(1-\dfrac{1}{2012}\right)=7.\dfrac{2011}{2012}=\dfrac{14077}{2012}\)

a) 17.13+17.42-17.35

=17.(13+42-35)

=17.20=340

b) [25.(18-4²)-10]:4+6

=(25.2-10):4+6

=40:4+6=16

c) 3⁶:3²+2³.2²-3².3

=3⁴+2⁵-3³

=81+32-27=86

d) B=3.4²-2².3

=3.(16-4)

=3.12=36

e)2022⁰+3.[5².10-(23-13)²]

=1+3.(250-100)

=1+450=451

g) 27.77+24.27-27

=27.(77+24-1)

=27.100=2700

h) 5.2³+7⁹:7⁷-1²⁰²⁰

=40+7²-1

=89-1=88

i) 120:{54[50:2+(3²-2.4)]}

=120:[54(25+1)]

=120:1404=10/117

Xét: 3/(1.2)=(1+2)/(1.2)=1/2+1

5/(2.3)=(2+3)/(2.3)=1/3+/1/2

7/(3.4)=(3+4)/(3.4)=1/4+1/3

...

2021/(1010.1011)=(1010+1011)/(1010.1011)=1/1010+1/1011

Do đó: Q=1+1/2-1/2-1/3+1/3+1/4-...-1/1010-1/1011

=1-1/1011

=1010/1011

sai thì sorry nha, nhưng cách làm là đúng rồi

Lê Gia Long e lớp 4 thì ko đc lm!

\(Q=\frac{3}{1\cdot2}-\frac{5}{2\cdot3}+\frac{7}{3\cdot4}...-\frac{2021}{1010\cdot1011}\)

\(=\left(\frac{1}{1}+\frac{1}{2}\right)-\left(\frac{1}{2}+\frac{1}{3}\right)+\left(\frac{1}{3}+\frac{1}{4}\right)...-\left(\frac{1}{1010}-\frac{1}{1011}\right)\)

\(=1-\frac{1}{1011}\)

\(=\frac{1010}{1011}\)

mik mơí lớp 4

 hihi

\(1-\dfrac{1}{x+1}=\dfrac{14}{15}\)

\(\dfrac{x+1-1}{x+1}=\dfrac{14}{15}\)

\(\dfrac{x}{x+1}=\dfrac{14}{15}\)

\(15x=14x+14\)

\(x=14\)

\(\Leftrightarrow2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{47}-\frac{1}{49}\right)+4x=7.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}\right)\)\(\Leftrightarrow2.\left(1-\frac{1}{49}\right)+4x=7.\left(1-\frac{1}{99}\right)\)

\(\Leftrightarrow2.\frac{48}{49}+4x=7.\frac{98}{99}\)

\(\Leftrightarrow\frac{96}{49}+4x=\frac{686}{99}\)

\(\Leftrightarrow4x=\frac{686}{99}-\frac{96}{49}\)

\(\Leftrightarrow4x=4,970109256\)

\(\Leftrightarrow x=4,970109256:4\)

\(\Leftrightarrow x=1,242527314\)

A=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=1/3-1/9

A=2/9

các câu 2;3 còn lại giống câu 1 bạn nhé

bạn thay số vào rồi làm tương tự

A=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=1/3-1/9

A=2/9.

7^3\(x-2\) -3.7³ = 7³.4

7^\(3x-2\)  = 7³.4 + 7³.3

7^3\(x-2\)  = 7³.(4 + 3)

7^{3x - 2}   = 7³.7

7^3\(x-2\) = 7⁴

3\(x\) - 2 = 4

 3\(x\)      = 4 + 2

3\(x\)        = 6

   \(x\)       = 6 : 3

   \(x\)       = 2