a) \(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3.4}+....+\dfrac{1}{299\cdot300}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{299}-\dfrac{1}{300}\)

\(=1-\dfrac{1}{300}=\dfrac{299}{300}\)

b) \(B=\dfrac{10^2}{16\cdot26}+\dfrac{10^2}{26\cdot36}+\dfrac{10^2}{36\cdot46}+...+\dfrac{10^2}{86.96}\)

\(\dfrac{B}{10}=\dfrac{10}{16\cdot26}+\dfrac{10}{26\cdot36}+\dfrac{10}{36\cdot46}+...+\dfrac{10}{86\cdot96}\)

\(\dfrac{B}{10}=\dfrac{1}{16}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{36}+\dfrac{1}{36}-\dfrac{1}{46}+...+\dfrac{1}{86}-\dfrac{1}{96}\)

\(\dfrac{B}{10}=\dfrac{1}{16}-\dfrac{1}{96}=\dfrac{5}{96}\)

\(\Rightarrow B=\dfrac{5}{96}\cdot10=\dfrac{25}{48}\)

Trong 5 khẳng định trên thì khẳng định (1),(3) đúng

Nhận xét

Quan hệ của (A-B)² với (B-A)²

\(\left(A-B\right)^2=\left(B-A\right)^2\)

Quan hệ của (A-B)³ với (B-A)³ : đối nhau

a) \(-x^3+3x^2-3x+1\)

\(-\left(x^3-3x^2+3x-1\right)\)

\(-\left(x-1\right)^3\)

b) \(8-12x+6x^2-x^3\)

\(=\left(2-x\right)^3\)

a)

\(\left(2x^2+3y\right)^3\)

\(=\left(2x^2\right)^3+3\left(2x^2\right)^2\cdot3y+3\cdot2x^2\cdot\left(3y\right)^2+\left(3y\right)^3\)

\(=8x^5+36x^4y+54x^2y^2+27y^3\)

b)

\(\left(\dfrac{1}{2}x-3\right)^3\)

\(=\left(\dfrac{1}{2}x\right)^3-3\cdot\left(\dfrac{1}{2}x\right)^2\cdot3+3\cdot\dfrac{1}{2}x\cdot9-27\)

\(=\dfrac{1}{8}x^3-\dfrac{9}{4}x^2+\dfrac{27}{2}x-27\)

\(\dfrac{x-1}{x^2-1}=\dfrac{x-1}{\left(x+1\right)\left(x-1\right)}=\dfrac{1}{x+1}\)

\(\Rightarrow\left\{{}\begin{matrix}a=1\\b=1\end{matrix}\right.\)

\(\Rightarrow a+b=1+1=2\)

He thuc nay o dinh ly 4 bai 1 ma

\(VP=\dfrac{1}{n}-\dfrac{1}{n+a}=\dfrac{n+a}{n\left(n+a\right)}-\dfrac{n}{n\left(n+a\right)}=\dfrac{a}{n\left(n+a\right)}=VT\)

a)\(\dfrac{6.9-2\cdot17}{63\cdot3-119}=\dfrac{2\cdot3\cdot9-2\cdot17}{7\cdot9\cdot3-7\cdot17}=\dfrac{2\cdot27-2\cdot17}{7\cdot27-7\cdot17}=\dfrac{2\left(27-17\right)}{7\left(27-17\right)}=\dfrac{2}{7}\)

b) \(\dfrac{3\cdot13-13\cdot18}{15\cdot40-80}=\dfrac{13\cdot\left(3-18\right)}{\left(15-2\right)\cdot40}=\dfrac{13\cdot\left(-15\right)}{13\cdot40}=-\dfrac{15}{40}=-\dfrac{3}{8}\)

c) \(\dfrac{25\cdot13}{26\cdot35}=\dfrac{5^2\cdot13}{2\cdot13\cdot5\cdot7}=\dfrac{5}{14}\)

2.All the workers of the plant were being instructed by the chief.

3. Some of my book have been taken away

4. The meeting will be held before May Day.

5. The engine of the car has to be repaired

6. Window was broken and some pictures were taken away by the boys

7. A lot of money was spent adverising everyday

8. This room may be used for the classroom

9. A story is going to be told by the teacher

10. The cake is being cut with a sharp knife by Mary.