\(\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)+\left(\frac{1}{2}+\frac{3}{4}+\frac{3}{4}\right)-2=?\)

what?

có kết quả là :

   ??????

  làm biến câu đầu trong () thứ nhất là :

      ??? 

Lời giải:

$1+2+3+...+n=n(n+1):2$

n(n+1):2

= n(n+1)/2

Đặt tổng trên là: \(A\)

\(A=\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}+\dfrac{3}{512}\)

\(\Rightarrow A.4=6+\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}\)

\(\Rightarrow A.4-A=\left(6+\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}\right)-\left(\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}+\dfrac{3}{512}\right)\)

\(\Rightarrow A.3=6-\dfrac{3}{512}=\dfrac{3069}{512}\)

\(\Rightarrow A=\dfrac{3069}{512}:3=\dfrac{1023}{512}\)

3/512 là gì vậy bn?

1. x( x - 3 ) + y( y - 3 ) + 2xy - 35

= x² - 3x + y² - 3y + 2xy - 35

= ( x² + 2xy + y² ) - ( 3x + 3y ) - 35

= ( x + y )² - 3( x + y ) - 35

= 5² - 3.5 - 35

= 25 - 15 - 35 = -25

2. 4x² + y² + 8x - 4xy - 4y + 100

= ( 4x² - 4xy + y² + 8x - 4y + 4 ) + 96

= [ ( 4x² - 4xy + y² ) + ( 8x - 4y ) + 4 ] + 96

= [ ( 2x - y )² + 2.( 2x - y ).2 + 2² ] + 96

= ( 2x - y + 2 )² + 96

= ( 4 + 2 )² + 96

= 6² + 96 = 36 + 96 = 132

Ta có : S = 1 - 2 + 2² - 2³ + .... - 2²⁰⁰⁹ + 2²⁰¹⁰

 => 2S = 2 - 2² + 2³ - 2⁴ + .... - 2²⁰¹⁰ + 2²⁰¹¹

Lấy 2S trừ S theo vế ta có : 

2S + S = (2 - 2² + 2³ - 2⁴ + .... - 2²⁰¹⁰ + 2²⁰¹¹) + (1 - 2 + 2² - 2³ + .... - 2²⁰⁰⁹ + 2²⁰¹⁰) 

       3S = 2²⁰¹¹ + 1

Khi đó 3S - 2²⁰¹¹ = 2²⁰¹¹ + 1 - 2²⁰¹¹ = 1  

ccđmvvh

a, \(5-\left(\frac{a}{b}+\frac{1}{2}\right)=2\frac{1}{3}\)   =>  \(\frac{a}{b}+\frac{1}{2}=5-2\frac{1}{3}\) =>  \(\frac{a}{b}+\frac{1}{2}=\frac{8}{3}\)  => \(\frac{a}{b}=\frac{8}{3}-\frac{1}{2}\) =>  \(\frac{a}{b}=\frac{13}{6}\)

b, \((\frac{3}{4}+2\frac{1}{2}):\frac{3}{5-3}=\left(\frac{3}{4}+\frac{5}{4}\right):\frac{3}{5}-1=\frac{9}{4}:\frac{-2}{5}=\frac{-45}{8}\)

a, 5-(\(\frac{a}{b}\)+\(\frac{1}{2}\))=2\(\frac{1}{3}\)

<=>5-\(\frac{a}{b}-\frac{1}{2}\)=\(\frac{7}{3}\)

<=>\(\frac{a}{b}=5-\frac{1}{2}-\frac{7}{3}\)

<=>\(\frac{a}{b}=\frac{13}{6}\)

b,(\(\frac{3}{4}\)+2\(\frac{1}{2}\)):\(\frac{3}{5}\)-3

=(\(\frac{3}{4}\)+\(\frac{5}{2}\)).\(\frac{5}{3}\)-3

=\(\frac{23}{4}\).\(\frac{5}{3}\)-3

=\(\frac{115}{12}\)-3

=\(\frac{115-36}{12}\)

=\(\frac{79}{12}\)

a) \(5-\left(\frac{a}{b}+\frac{1}{2}\right)=2\frac{1}{3}\)

\(\Rightarrow5-\left(\frac{a}{b}+\frac{1}{2}\right)=\frac{7}{3}\)

\(\Rightarrow\frac{a}{b}+\frac{1}{2}=5-\frac{7}{3}\)

\(\Rightarrow\frac{a}{b}+\frac{1}{2}=\frac{8}{3}\)

\(\Rightarrow\frac{a}{b}=\frac{8}{3}-\frac{1}{2}\)

\(\Rightarrow\frac{a}{b}=\frac{13}{6}\)

Vậy \(\frac{a}{b}=\frac{13}{6}\)

b) \(\left(\frac{3}{4}+2\frac{1}{2}\right):\frac{3}{5}-3\)

\(=\left(\frac{3}{4}+\frac{5}{2}\right):\frac{3}{5}-3\)

\(=\frac{13}{4}:\frac{3}{5}-3\)

\(=\frac{65}{12}-3\)

\(=\frac{29}{12}\)

Học tốt #

58.2417353404 nha bn ! 

hok tốt thi tốt

=9.31+9.9-40.9

=9.(31+9-40)

=9.0

=0

Ta có : 3².31+9.3²-40.9

= 3².31+9.3²-40.3²

= 3². ( 31+9-40 ) = 3².0 =0

y :3 :2 = 16

y : 3 = 16 x2

y : 3 = 32

y = 32 x 3

y = 96

Y:3=16*2=32

Y=32*3=96

96 nhé