Xét : \(\left(\frac{1}{k-1}-\frac{1}{k}+1\right)^2=\frac{1}{k^2}+\frac{1}{\left(k-1\right)^2}+1+2\left(-\frac{1}{k\left(k-1\right)}-\frac{1}{k}+\frac{1}{k-1}\right)\)

\(=\frac{1}{k^2}+\frac{1}{\left(k-1\right)^2}+1\)

\(\Rightarrow\sqrt{1+\frac{1}{\left(k-1\right)^2}+\frac{1}{k^2}}=\left|\frac{1}{k-1}-\frac{1}{k}+1\right|\)với k thuộc N* , k > 1

Áp dụng : \(\sqrt{\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{4^2}}+...+\sqrt{\frac{1}{1^2}+\frac{1}{1999^2}+\frac{1}{2000^2}}\)

\(=\left(1+\frac{1}{2}-\frac{1}{3}\right)+\left(1+\frac{1}{3}-\frac{1}{4}\right)+...+\left(1+\frac{1}{1999}-\frac{1}{2000}\right)\)

\(=1998+\frac{1}{2}+-\frac{1}{2000}\)

1. He said, "I am going to town with my sister"

=> He said he was going to town with his sister

2. He said to her, "you are wearing your best clothes"

=>He said to her that she was wearing her best clothes

3. They said, "We are unlucky today"

=> They said they were unlucky that day

4. She said to me, "I want to speak to your brother"

=> She said to me that she wanted to speak to my brother

5. She said, "I have helped my mother"

=> She said she had helped her mother

6. John said to Mary, "She is ready to go with us"

=> John said to Mary that she was ready to go with them

7. She said to me , "they do not know you"

=> She said to me that they didn't know you

8. He said, "I shall answer the phone"

=> He said he would answer the phone

9. She said to them, "You can do it if you try"

=>  She said to them that they could do it if they try

10. He said, "He has done his homework well"

=> He said he had done his homework well

1. As I (cross) crossed the road and I (step) stepped on a banana skin and (fall) falled heavily

2. When he (mend) mended the fuse, he (get) got a very bad shock

3. While the gustes (dance) were dancing, thieves (break) broke into the house and (steal) stole a lot of fur coats

4. The next day, as they (know) knew that the police (look) would look for them, they (hide) hid the coats in a wood and (go) went off in different directions

5. She was very extravagant. She always (buy) buys herself new clothes

6. Her mother often (tell) tells her that she (spend) spends too much money but she never (listen) listens

7. Whenver the drummer (begin) begins practising, the people in the next flat (bang) bang on the wall

8. To get home he (have to) has to go through a field where a bad-tempered bull usually (graze) grazes

9. This (annoy) annoys the bull, who immediatekly (begin) begins to chase Mr.Smith

10. I (be) am sorry that I (have to) have to leave the party early, because I (enjoy) enjoy myself

Gọi x và y lần lượt là số mol Fe và Al tham gia phản ứng

a/PTHH: Fe + H₂SO₄ -----> FeSO₄ + H₂

(mol)       x         x                  x            x

  PTHH:  2Al + 3H₂SO₄ -----> Al₂(SO₄)₃ + 3H₂

(mol)       y         3y/2                 y/2           3y/2

Suy ra hệ : \(\begin{cases}152x+\frac{342y}{2}=81,7\\56x+27y=19,3\end{cases}\) \(\Leftrightarrow\begin{cases}x=0,2\\y=0,3\end{cases}\)

=> mFe = 0,2.56 = 11,2 (g)

\(\Rightarrow\%Fe=\frac{11,2}{19,3}.100\approx58,03\%\)

%Al = 100% - 58,03% = 41,97%

b/ nH₂ = x+3y/2 = 0,2 + 3.0,3/2 = 0,65 (mol)

=> VH₂ = 22,4.0,65 = 14,56 (l)

c/  nH₂SO₄ = x+3y/2 = 0,65 (mol)

=> mH₂SO₄ = 98.0,65 = 63,7 (g)

a/ Gọi x,y lần lượt là số mol CuO và ZnO tham gia phản ứng

nHCl = 14,6/36,5 = 0,4 (mol)

PTHH : CuO + 2HCl -----> CuCl₂ + H₂O

 (mol)      x         2x               x

             ZnO + 2HCl -----> ZnCl₂ + H₂O

(mol)        y        2y               y

Ta có hệ pt : \(\begin{cases}80x+81y=16,08\\2x+2y=0,4\end{cases}\) \(\Leftrightarrow\begin{cases}x=0,12\\y=0,08\end{cases}\)

=> mCuO = 0,12.80 = 9,6 (g)

\(\Rightarrow\%CuO=\frac{9,6}{16,08}.100\approx59,7\%\)

=> %ZnO = 100% - 59,7% = 40,3%

b/ mCuCl₂ = 0,12.135 = 16,2(g)

mZnCl₂ = 0,08.136 = 10,88 (g)

a/ \(CO_2+Ca\left(OH\right)_2\rightarrow CaCO_3+H_2O\)

b/ \(2H_2O_2\rightarrow2H_2O+O_2\)

c/ \(CaCO_3\rightarrow^{t^0}CaO+CO_2\)

Chu vi hình vuông là:

    20 x 4 = 80 (m)

Diện tích hình vuông là:

    20 x 20 = 400 (m2)

             Đáp số: Chu vi : 80 m

                         Diện tích : 400 m2

a/ Gọi điểm cố định là N(x₀;y₀)

Suy ra N thuộc đồ thị hàm số y = (m-2)x+3 nên : 

\(y_0=\left(m-2\right)x_0+3\Leftrightarrow mx_0-\left(2x_0+y_0-3\right)=0\)

Vì đths luôn đi qua N với mọi x,y nên : 

\(\begin{cases}x_0=0\\2x_0+y_0-3=0\end{cases}\) \(\Leftrightarrow\begin{cases}x_0=0\\y_0=3\end{cases}\)

Vậy điểm cố định là \(N\left(0;3\right)\)

b,c tương tự

Nhưng mà mình thấy trieu dang trả lời đầu tiên

Đặt \(t=\left|x-1\right|,t\ge0\)

Suy ra pt trở thành : \(t^2+t-2016=0\)

Xét \(\Delta=1^2-4.\left(-2016\right)=8065\)

\(\Rightarrow\begin{cases}t_1=\frac{-1-\sqrt{8065}}{2}\left(\text{loại}\right)\\t_2=\frac{-1+\sqrt{8065}}{2}\left(\text{nhận}\right)\end{cases}\)

Ta có \(\left|x-1\right|=\frac{-1+\sqrt{8065}}{2}\)

+ Nếu \(x\ge1\) thì \(x-1=\frac{-1+\sqrt{8065}}{2}\Rightarrow x=\frac{1+\sqrt{8065}}{2}\)(tm)

+ Nếu x < 1 thì \(1-x=\frac{-1+\sqrt{8065}}{2}\Rightarrow x=\frac{3-\sqrt{8065}}{2}\) (tm)