Gọi biểu thức trên là A, ta có:

\(A=\frac{1}{2\cdot15}+\frac{1}{15\cdot3}+\frac{1}{3\cdot21}+\frac{1}{21\cdot4}+...+\frac{1}{87\cdot90}\)

\(13A=\frac{13}{2\cdot15}+\frac{13}{15\cdot3}+\frac{13}{3\cdot21}+\frac{13}{21\cdot4}+...+\frac{13}{87\cdot90}\)

\(13A=\frac{1}{2}-\frac{1}{15}+\frac{1}{15}-\frac{1}{3}+\frac{1}{3}-\frac{1}{21}+\frac{1}{21}-\frac{1}{4}+...+\frac{1}{87}-\frac{1}{90}\)

\(13A=\frac{1}{2}-\frac{1}{90}\)

\(13A=\frac{22}{45}\)

\(A=\frac{22}{45\text{x}13}=\frac{22}{585}\)

sai r

\(x=\)dấu nhân hả bạn ?

\(\frac{A}{6}=\frac{1}{12\times15}+\frac{1}{15\times18}+\frac{1}{18\times21}+...+\frac{1}{87\times90}\)

\(\frac{A}{6}=\frac{1}{3}\times\left(\frac{3}{12\times15}+\frac{3}{15\times18}+\frac{3}{18\times21}+...+\frac{3}{87\times90}\right)\)

\(\frac{A}{6}=\frac{1}{3}\times\left(\frac{1}{12}-\frac{1}{15}+\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(\frac{A}{6}=\frac{1}{3}\times\left(\frac{1}{12}-\frac{1}{90}\right)=\frac{1}{3}\times\frac{13}{180}=\frac{13}{540}\)=> A = \(\frac{13}{90}\)

X là dấu nhân đúng không.

\(B=\frac{1}{1x2x5}+\frac{1}{2x3x4}+\frac{1}{3x4x5}+...+\frac{1}{98x99x5}+\frac{1}{99x100x5}\)

\(5B=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{98x99}+\frac{1}{99x100}\)

\(5B=\frac{2-1}{1x2}+\frac{3-2}{2x3}+\frac{4-3}{3x4}+...+\frac{99-98}{98x99}+\frac{100-99}{99x100}\)

\(5B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

\(5B=1-\frac{1}{100}=\frac{99}{100}\Rightarrow B=\frac{99}{500}\)

a) A = 9/8.11 + 9/11.14 + 9/14.17 + ... + 9/73.75

A = 3.(1/8 - 1/11 + 1/11 - 1/14 + 1/14 - 1/17 + ... + 1/73 - 1/75)

A = 3.(1/8 - 1/75)

A = 3.67/600

A = 67/200

Các bài sau làm tương tự, riêng câu D thì phân tích ra 

Mình chỉ làm hộ bạn câu a) thôi nhé vì đề sàn sàn giống nhau :

a) \(A=\frac{9}{8×11}+\frac{9}{11×14}+\frac{9}{14×17}+...+\frac{9}{73×75}\)

\(A=\frac{9}{8}-\frac{9}{11}+\frac{9}{11}-\frac{9}{14}+\frac{9}{14}-\frac{9}{17}+...+\frac{9}{73}-\frac{9}{75}\)

\(A=\frac{9}{8}-\frac{9}{75}\)

\(A=\frac{675}{600}-\frac{72}{600}\)

\(A=\frac{673}{600}\)

Vậy,...

Cbht

\(d,D=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

\(10D=\frac{1}{7\cdot8}+\frac{1}{2\cdot70}+\frac{1}{2\cdot130}+...+\frac{1}{2\cdot700}\)

\(10D=\frac{1}{7}-\frac{1}{8}+\frac{1}{2}-\frac{1}{70}+\frac{1}{2}-\frac{1}{130}+...+\frac{1}{2}-\frac{1}{700}\)

\(10D=\frac{1}{7}-\frac{1}{700}\)

\(10D=\frac{99}{700}\)

\(D=\frac{99}{700}:10\)

\(D=\frac{99}{7000}\)

gợi ý nè

1/a.b=1/a-1/b

b. B= 1/25×27+1/27×29+1/29×31+...+1/73×75

2B= 2.(1/25×27+1/27×29+1/29×31+...+1/73×75)

2B= 2/25×27+2/27×29+2/29×31+...+2/73×75

2B= 1/25-1/27+1/27-1/29+...+1/73-1/75

2B= 1/25-1/75

B=(1/25-1/75):2

Từng đó đã nha để mik nghĩ tiếp

T.i.c.k đc ko PLEASE!!!

5/2\(\times\)1=\(\frac{5}{2\times1}hay=\frac{5}{2}\times1\)

Lời giải:
a. $(x+y)-(x-y)=x+y-x+y=(x-x)+y+y=0+2y=2y$

b. $3x(5x^2-2x-1)-15x^3=15x^3-6x^2-3x-15x^3=-6x^2-3x$
c. $(5x-2y)(x^2-xy+1)+7x^2y=5x^3-5x^2y+5x-2x^2y+2xy^2-2y+7x^2y$

$=5x^3+(-5x^3y-2x^2y+7x^2y)+5x+2xy^2-2y$

$=5x^3+5x+2xy^2-2y$