Ta có:

\(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\)

\(=\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\)

\(=\frac{1}{18}-\frac{1}{126}=\frac{1}{21}\)

1/21 nha pn

a) đặt  \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}+\frac{1}{256}\)

\(\Rightarrow2\times A=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{128}\)

\(\Rightarrow2\times A-A=1-\frac{1}{256}\)

\(A=\frac{255}{256}\)

phần b bn cx lm tương tự như z nha!

c) sửa đề:

\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{13x14}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{13}-\frac{1}{14}\)

\(=1-\frac{1}{14}=\frac{13}{14}\)

Sửa:

d) \(\frac{1}{15x18}+\frac{1}{18x21}+\frac{1}{21x24}+...+\frac{1}{87x90}\)

\(=\frac{1}{3}x\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(=\frac{1}{3}x\left(\frac{1}{15}-\frac{1}{90}\right)\)

\(=\frac{1}{3}x\frac{1}{18}\)

\(=\frac{1}{54}\)

A.3=5.3/18.21+5.3/21.24+5.3/24.27+...+5.3/123.126

A.3=5/18-5/21 +  5/21-5/24 + 5/24-5/27 +...+ 5/123-5/126

A.3=5/18-5/126

A.3=   5/21

A  =5/21:3

A  =  5/63

    Đây là cách của mik nếu sai thì thôi nhé

Kết quả đúng rồi đấy !

A=5/3 x (3/(18x21) + 3/(21x24) + 3/(24x27) + ... + 3/(123x 126)

A=5/3 x (1/18 - 1/21 + 1/21 - 1/24 + 1/24 - 1/27 +...+1/ 123 - 1/ 126)

A=5/3x(1/8-1/126)

A=5/3x 1/21

A=5/63

 B8 = 6/15.18 + 6/18.21 + 6/21.24 + ... + 6/87.90

 B8 = 2.(3/15.18 + 3/18.21 + 3/21.24 + ... + 3/87 .90)

 B8 = 2.(1/15 - 1/18 + 1/18 -1/21 + 1/21 - 1/24 + ... + 1/87 - 1/90)

 B8 = 2.(1/15 - 1/90)

 B8 = 2.(6/90 - 1/90)

 B8 = 2. 1/18

 B8 = 1/9

 B = 1/9 : 8

 B = 1/72

thank bạn nha

Gọi tổng bằng S

1/9 S=1/15*18+..................+1/87*90

1/9 S=1/15-1/18+1/18-......................-1/90

1/9 S=1/15-1/90

1/9 S=1/18

S=9/18=1/2

bạn sai ở đoạn cuối

A=\(\frac{3\cdot3}{15\cdot18}+\frac{3\cdot3}{18\cdot21}+...+\frac{3\cdot3}{96\cdot99}=3\cdot\left(\frac{3}{15\cdot18}+\frac{3}{18\cdot21}+...+\frac{3}{96\cdot99}\right)=3\cdot\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{96}-\frac{1}{99}\right)=3\cdot\left(\frac{1}{15}-\frac{1}{99}\right)=3\cdot\frac{28}{495}=\frac{28}{165}\)

64200 

45360

38090

3

3

57

= 64200 

= 45360

= 38090

= 3

= 3

= 57

64200 

45360

38090

3

3

57

thay x = 122 vào biểu thức A(x) = x⁴ - 123x³ + 123x² - 123x + 125 ta có :

A(x) = 122⁴ - 123.122³ + 123.122² - 123.122 + 125

= 221533456 - 223349304 + 1830732 - 15006 + 125

= 3

1) x-12=(-8)+(-17)
    x-12=(-25)
    x      = (-25)+12
    x      = (-13)