Ta có : \(\frac{1}{a}-\frac{1}{b}=\frac{2}{3}\)

\(\Leftrightarrow\frac{b}{ab}-\frac{a}{ab}=\frac{2}{3}\)

\(\Leftrightarrow\frac{b-a}{ab}=\frac{2}{3}\)

<=> \(\frac{2}{ab}=\frac{2}{3}\)

<=> ab = 3

Nên : a,b thuộc Ư(3) = {1;3}

Mà b - a = 2 

Vậy a = 1 thì b = 3

Thanks anh Hoàng CTV!

Ta có: a,bc : ( a + b + c) = 0,25
Biến đổi: abc = 25( a+ b + c) 
=> abc chia hết cho 25
=> bc = 25, bc = 50 hoặc bc = 75
Nếu bc = 25 thì a25 = 25( a+ 7)
=> 100a + 25 = 25a + 175
=> 75a = 150
=> a = 2 ( loại, vì a =b =2)
Nếu bc = 50 thì a50 = 25( a+ 5)
=> 100a + 50 = 25a + 125
=> 75a = 75
=> a = 1
Nếu bc = 75 thì a75 = 25( a+ 12)
=> 100a + 75 = 25a + 300
=> 75a = 225
=> a = 3
Có hai đáp án:
1,50 : ( 1 + 5 + 0) = 0,25
3,75 : ( 3 + 7 + 5 ) = 0,25

\(\overline{abc}\) : ( a + b + c ) = 25

\(\Rightarrow\)\(\overline{abc}\)= 25(a+b+c)

\(\Rightarrow\overline{abc=25a+25b+25c}\)

\(\Rightarrow100a+10b+c=25a+25b+25c\)

\(\Rightarrow75a=15b+24c\)

\(\Rightarrow75=75+0\)

\(\Rightarrow a=75:75=1;b=75:15=5;c=0:24=0\)

Vậy a = 1 ; b = 5 ; c = 0 ; \(\overline{abc=150}\)

Đặt \(A=3^2+3^3+3^4+...+3^{101}\)

\(A=\left(3^2+3^3+3^4+3^5\right)+\left(3^6+3^7+3^8+3^9\right)+...+\left(3^{98}+3^{99}+3^{100}+3^{101}\right)\)

\(A=3\left(3+3^2+3^3+3^4\right)+3^5\left(3+3^2+3^3+3^4\right)+...+3^{97}\left(3+3^2+3^3+3^4\right)\)

\(A=3.\left(3+9+27+81\right)+3^5\left(3+9+27+81\right)+...+3^{97}\left(3+9+27+81\right)\)

\(A=3.120+3^5.120+...+3^{97}.120\)

\(A=120\left(3+3^5+...+3^{97}\right)⋮120\)

Vậy \(A⋮120\)

Chúc bạn học tốt ~ 

Ta có : 

\(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right).....\left(1-\frac{1}{10^2}\right)\)

\(=\)\(\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.\frac{4^2-1}{4^2}.....\frac{10^2-1}{10^2}\)

\(=\)\(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{9.11}{10.10}\)

\(=\)\(\frac{1.3.2.4.3.5.....9.11}{2.2.3.3.4.4.....10.10}\)

\(=\)\(\frac{\left(1.2.3.....9\right).\left(3.4.5.....11\right)}{\left(2.3.4.....10\right).\left(2.3.4.....10\right)}\)

\(=\)\(\frac{11}{2.10}\)

\(=\)\(\frac{11}{20}\)

Chúc bạn học tốt ~ 

(1-1/2^2)(1-1/3^2)(1-1/4^2)....(1-1/10^2)

=3/4.8/9.15/16...99/100

Từ đó tính kết quả là ok

1/2²<1/1.2

1/3²<1/2.3

.....<.......

1/2018²<1/2017.2018

=>1/2²+1/3²+....+1/2018²<1/1.2+1/2.3+...+1/2017.2018=1/1-1/2+1/2-1/3+...+1/2017-1/2018=1-1/2018<1

=>1/2²+1/3²+....+1/2018²<1 (đpcm)

A = \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2018^2}\)<  \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)

=> \(A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)

=> \(A< 1-\frac{1}{2018}< 1\)=>  \(A< 1\)( đpcm )

A = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + ... + 2013 + 2014 - 2015 - 2016

A = ( 1 + 2 - 3 - 4 ) + ( 5 + 6 - 7 - 8 ) + ... + ( 2013 + 2014 - 2015 - 2016 )

A = (-4) + (-4) + ... + (-4)

A = (-4) . 504

A = (-2016)

Vậy A = (-2016).

~~~

A=1+(2-3-4+5) +(6-7-8+9)+...+(2014-2015-2016+2017)-2017=1-2017=-2016

tren cung mot nua mat phang bo chua tia ox co 
xot=40
xoy=80
xot<xoy
nen ot nam giua 2 tia ox va oy
B,vi ot nam giua 2 tia ox va oy 
nen xot + yot=xoy
ma xot= 40
xoy=80
nen 40+yot=80
yot=80-40
yot=40
C,ta co xot=40
yot=40
nen xot =yot
ma ot nam giua 2 tia ox va oy
nen ot la tia phan giac cua xoy
cau b phai la xoz chu ko phai xox dau ban a 

vi oz la tia phan giac cua yot
nen zot=1\2 yot
ma yot=40
nen zot=1\2.40
zot=20
vi ot nam giua 2 tia ox va oy
oz nam giua 2tia oy va ot
nen ot nam giua 2 tia ox vaoz
dodo xoz= zot+xot
ma zot=20
xot=40
nen xoz=20+40
xoz=60
vay xoz=60 

xx

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Bài 1 : dễ bạn tự làm được :) 

Bài 2 : 

Ta có : 

\(B=\frac{2015+2016+2017}{2016+2017+2018}=\frac{2015}{2016+2017+2018}+\frac{2016}{2016+2017+2018}+\frac{2017}{2016+2017+2018}\)

Vì : 

\(\frac{2015}{2016}>\frac{2015}{2016+2017+2018}\)

\(\frac{2016}{2017}>\frac{2016}{2016+2017+2018}\)

\(\frac{2017}{2018}>\frac{2017}{2016+2017+2018}\)

Nên \(\frac{2015}{2016}+\frac{2016}{2017}+\frac{2017}{2018}>\frac{2015}{2016+2017+2018}+\frac{2016}{2016+2017+2018}+\frac{2017}{2016+2017+2018}\)

\(\Leftrightarrow\)\(\frac{2015}{2016}+\frac{2016}{2017}+\frac{2017}{2018}>\frac{2015+2016+2017}{2016+2017+2018}\)

\(\Leftrightarrow\)\(A>B\)

Vậy \(A>B\)

Chúc bạn học tốt ~ 

Ta có :  B = 2016 + 2017 + 2018 2015 + 2016 + 2017 = 2016 + 2017 + 2018 2015 + 2016 + 2017 + 2018 2016 + 2016 + 2017 + 2018 2017 Vì :  2016 2015 > 2016 + 2017 + 2018 2015 2017 2016 > 2016 + 2017 + 2018 2016 2018 2017 > 2016 + 2017 + 2018 2017 Nên  2016 2015 + 2017 2016 + 2018 2017 > 2016 + 2017 + 2018 2015 + 2016 + 2017 + 2018 2016 + 2016 + 2017 + 2018 2017 ⇔ 2016 2015 + 2017 2016 + 2018 2017 > 2016 + 2017 + 2018 2015 + 2016 + 2017 ⇔A > B Vậy A > B Chúc bạn học tốt ~ 

A = -1 - 2 + 3 + 4 - 5 - 6 + 7 + 8 - 9 - 10 + 11 + 12 - ... - 2013 - 2014 + 2015 + 2016

=> A = (-1 - 2 + 3 + 4) + (-5 - 6 + 7 + 8) + (-9 - 10 + 11 + 12) + ... + (-2013 - 2014 + 2015 + 2016)

=> A = 4 + 4 + 4 + ... + 4

           có 2016 : 4 = 504 (số 4)

=> A = 4 . 504

=> A = 2016