a)

Vì 2/9=6/27=8/36=12/54=16/72=18/81 nên:

2/9+6/27+8/36+12/54+16/72+18/81=

2/9+2/9+2/9+2/9+2/9+2/9=

2/9*6=

12/9=

4/3

Vậy 2/9+6/27+8/36+12/54+16/72+18/81=4/3

b)

Ta có:

1-2/5=3/5

1-2/7=5/7

1-2/9=7/9

...

1-2/99=97/99

Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=

3/5*5/7*7/9*...*97/99=

(3*5*7*...*97)/(5*7*9*...*99)=

3/99=

1/33

Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=1/33

c)

Gọi biểu thức 1/2+1/4+1/8+1/16+...+1/1024 là S,ta có:

S=1/2+1/4+1/8+1/16+...+1/1024

S*2=1+1/2+1/4+1/8+...+1/512

S*2-S=(1+1/2+1/4+1/8+...+1/512)-(1/2+1/4+1/8+1/16+...+1/1024)

S=1-1/1024

S=1023/1024

Vậy 1/2+1/4+1/8+1/16+...+1/1024=1023/1024

Cảm ơn bạn nhé!

1-4+7-10+....+31-34=(1-4)+(7-10)+....+(31-34)=-3+(-3)+.....+(-3) (có 12 số -3)

=-3.12=-36

tick nha

-36

\(\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}\)

\(=\left(\frac{12}{8}+\frac{3}{8}\right)+\left(\frac{12}{128}+\frac{3}{128}\right)+\frac{3}{512}\)

\(=\frac{15}{8}+\frac{15}{128}+\frac{3}{512}\)

\(=\frac{240}{128}+\frac{15}{128}+\frac{3}{512}\)

\(=\frac{255}{128}+\frac{3}{512}\)

\(=\frac{1020}{512}+\frac{3}{512}\)

\(=\frac{1023}{512}\)

\(\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}=\frac{3}{1.2}+\frac{3}{2.4}+\frac{3}{4.8}+\frac{3}{8.16}+\frac{3}{16.32}\)
                                                        \(=\frac{3}{1}-\frac{3}{2}+\frac{3}{2}-\frac{3}{4}+\frac{3}{8}-\frac{3}{8}+\frac{3}{16}-\frac{3}{16}+\frac{3}{32}\)
                                                         \(=3+\frac{3}{32}=\frac{3.32}{32}+\frac{3}{32}=\frac{96+3}{32}=\frac{99}{32}\)

\(S=\frac{2+2^2+...+2^{2008}}{1-2^{2009}}\)

=>2S=\(\frac{2+2^2+...+2^{2009}}{1-2^{2009}}\)

=>2S-S=\(\frac{2+2^2+...+2^{2009}-1-2-2^2-...-2^{2008}}{1-2^{2009}}\)

S=\(\frac{2^{2009}-1}{1-2^{2009}}\)

=>S= -1

1.S1=1 - 2 + 3 - 4 + ... + 1997 - 1998 + 1999

       = (1 - 2) + ...+(1997 - 1998) + 1999

       = -1 + -1 + ...+-1 + 1999

 SH:1998 : 2

        = 999 . -1

        = -999

 TDS:-999 + 1999

        = 1000

b.S2=1 - 4 + 7 - 10 + ...- 2998+3001

       = (1 - 4) + (7 - 10) + ...+ (2995 - 2998) + 3001

       = -3 + -3 + ...+-3 + 3001

       = (2998 - 1) : 3 + 1

       = 1000 . -3

       = -3000 + 3001

       = 1

câu b mình làm lộn :

S2=1000 : 2 

    = 500 . -3

    =-1500 + 3001

    = 1501 

KẾT QUẢ RA 1501 NHA

Ta có: A = 1.2.3 + 2.3.4 + 3.4.5 + ... + 18.19.20
=> 4A = 4(1.2.3 + 2.3.4 + 3.4.5 + ... + 18.19.20)
=> 4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 +...... +18.19.20.4
=> 4A = 1.2.3.4 + 2.3.4(5 - 1) + 3.4.5.(6 - 2) +..... +18.19.20.(21 - 17)
=> 4A = 1.2.3.4 + 2.3.4.5 - 2.3.4 + 3.4.5.6 - 2.3.4.5 + ..... + 17.18.19.20 - 17.18.19.20
=> 4A =18.19.20
=> 4A = 6840
=> A = 1710

Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+18.19.20

4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+18.19.20)4

4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+18.19.20.(21-17)

4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+ 18.19.20.21-17.18.19.20
=>A =18.19.20.21

=>A+18.19.20.21/4

=> A=35910

Câu 1 :Liệt kê và tính tổng các sô nguyên x , biết :

     -8<x<9

=> x E { -7;-6;-5;-4;-3;-2;-1;0;1;2;3;4;5;6;7;8}

Đặt  -7;-6;-5;-4;-3;-2;-1;0;1;2;3;4;5;6;7;8 là A:

A=-7+(-6)+(-5)+(-4)+(-3)+(-2)+(-1)+0+1+2+3+4+5+6+7+8

A=(-7+7)+(-6+6)+(-5+5)+(-4+4)+(-3+3)+(-2+2)+(-1+1)+0+8

A=0+0+0+0+0+0+0+0+8

A=8

Câu 2 : Thực hiện phép tính ( Tính nhanh nếu có thể )

a.100+(+430)+2145+(-530)

=[100+430+(-530)]+2145

=0+2145

=2145

b.(-12).15=-180

c.(+12).13+13.(-22)

=13.[12+(-22)]

=13.(-10)

=-130

d.63.(-47)+(-63).53

=63.(-47)+63.(-53)

=63.[-47+(-53)]

=63.(-100)

=-6300

bạn làm đúng rồi nhé

chúc bạn học tốt@

a

\(\frac{3}{4}+\frac{1}{5}\)

\(=\frac{15}{20}+\frac{4}{20}\)

\(=\frac{19}{20}\)

b 

\(\frac{1}{36}+\frac{5}{12}\)

\(\frac{5}{12}=\frac{5\times3}{12\times3}=\frac{15}{36}\)

\(\frac{1}{36}+\frac{15}{36}=\frac{16}{36}=\frac{4}{9}\)

c

\(\frac{3}{4}+\frac{1}{6}\)

\(=\frac{18}{24}+\frac{4}{24}\)

\(=\frac{22}{24}=\frac{12}{11}\)

TL

a)3/4+1/5=19/20

b)1/36+5/12=4/9

c) 3/4+1/6=11/12

HT