Ta có: \(-1=-2+1;-\frac{1}{2}=-1+\frac{1}{2};-\frac{1}{4}=-\frac{1}{2}+\frac{1}{4};...;-\frac{1}{1024}=-\frac{1}{512}+\frac{1}{1024}\)

\(\Rightarrow-1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-...-\frac{1}{1024}\)

\(=\left(-2+1\right)+\left(-1+\frac{1}{2}\right)+\left(-\frac{1}{2}+\frac{1}{4}\right)\)\(+...+\left(-\frac{1}{512}+\frac{1}{1024}\right)\)

\(=-2+1-1+\frac{1}{2}-\frac{1}{2}+\frac{1}{4}-...-\frac{1}{512}+\frac{1}{1024}\)

\(=-2+\frac{1}{1024}\)

\(=-\frac{2047}{1024}\)

có kết quả r mà

\(\frac{8}{9}-\frac{1}{72}-\frac{1}{56}-...-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

\(=\frac{8}{9}-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{56}+\frac{1}{72}\right)\)

\(=\frac{8}{9}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{7.8}+\frac{1}{8.9}\right)\)

\(=\frac{8}{9}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)

\(=\frac{8}{9}-\left(1-\frac{1}{9}\right)\)

\(=\frac{8}{9}-\frac{8}{9}=0\)

thank you nhìu

a)

`9/2-3`

`=9/2-6/2`

`=3/2`

b)

`8/5xx25/12`

`=10/3`

c)

`4:3/7`

`=4xx7/3`

`=28/3`

thank you bạn

\(\left(1-\dfrac{1}{2}\right)\cdot\left(1-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{4}\right)\cdot...\cdot\left(1-\dfrac{1}{99}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5}\cdot...\cdot\dfrac{97}{98}\cdot\dfrac{98}{99}\)

\(=\dfrac{1\cdot2\cdot3\cdot...\cdot98}{2\cdot3\cdot4\cdot...\cdot99}\)

\(=\dfrac{1}{99}\)

\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}.....\dfrac{99}{98}.\dfrac{100}{99}=\dfrac{100}{2}=50\)

S1=1+(-2)+(-3)+4+5+(-6)+(-7)+8+...+1997+(-1998)+(-1999)+2000

S1=(1+4-2-3)+(5+8-6-7)+...+(1997+2000-1998-1999)

S1=0+0+...+0

S1=0

câu 2

S2=1+3+4+5+...+99-(2+4+6+...+100)

S2=51.50-(50.51)

S2=0

tich nha

tra goole bn ơi ai tick ủng hộ nha

1/3 - 1/4 = 4/12 - 3/12 = 1/12

2/7 . 14/5 - 1 = 2.14/7.5 - 1 =4/5 - 1 = -1/5

3/4 - 1/25 x 5 = 3/4 - 1.5/25.1 = 3/4 - 1/5 = 11/20

-8 . ( 6. 1/24 ) = -8 . ( 6.1/24.1 ) = -8 . 1/4 = -8 . 1/4.1 = -2

1/3-1/4=1/12

2/7.14/5-1=-1/5

3/4-1/25.5=11/20

-8.(6.1/24)=-2 nhé

CHÚC BẠN HỌC GIỎI

K MÌNH NHÉ

Ta có:\(\frac{1}{2}>\frac{1}{8};\frac{1}{3}>\frac{1}{8};...;\frac{1}{6}>\frac{1}{8};\frac{1}{7}+\frac{1}{8}+\frac{1}{9}>\frac{3}{8}\)

\(\Rightarrow\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}>\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{3}{8}\)

                                                                 \(=\frac{8}{8}=1\)

Vậy\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}>1\)