Bài 1: Tính

a. \(\left(1+\frac{1}{1\cdot3}\right)\cdot\left(1+\frac{1}{2\cdot4}\right)\cdot\left(1+\frac{1}{3\cdot5}\right)+\left(1+\frac{1}{4\cdot6}\right).....\left(1+\frac{1}{99\cdot101}\right)\)

b. \(\left[\sqrt{0,64}+\sqrt{0,0001}-\sqrt{\left(-0,5\right)^2}\right]\div\left[3\cdot\sqrt{\left(0,04\right)^2}-\sqrt{\left(-2\right)^4}\right]\)

c. \(\frac{5.4^{15}\cdot9^9-4.3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}-\frac{2^{19}\cdot6^{15}-7\cdot6^{10}\cdot2^{20}\cdot3^6}{9\cdot6^{19}\cdot2^9-4\cdot3^{17}\cdot2^{26}}+0,\left(6\right)\)

Bài 2: Tìm x, y, z biết :
a. \(\left(x-10\right)^{1+x}=\left(x-10\right)^{x+2009}\left(x\in Z\right)\)

b. \(\left|x-2007\right|+\left|x-2008\right|+\left|y-2009\right|+\left|x-2010\right|=3\left(x,y\in N\right)\) 

c. \(25-y^2=8\left(x-2009\right)^2\left(x,y\in Z\right)\)

d. \(2008\left(x-4\right)^2+2009\left|x^2-16\right|+\left(y+1\right)^2\le0\)

e. \(2x=3y\) ; \(4z=5x\) và \(3y^2-z^2=-33\)

Bài 3: Chứng minh rằng

a. \(1-\frac{1}{2^2}-\frac{1}{3^2}-\frac{1}{4^2}-...-\frac{1}{2009^2}>\frac{1}{2009}\)

b. \(\left[75\cdot\left(4^{2008}+4^{2007}+4^{2006}+...+4+1\right)+25\right]⋮100\)

Bài 4: 

a. Tìm giá trị nhỏ nhất của biểu thức : \(M=\left(x^2+2\right)+\left|x+y-2009\right|+2005\)

b. So sánh: \(31^{11}\) và \(\left(-17\right)^{14}\)

c. So sánh: \(\left(\frac{9}{11}-0,81\right)^{2012}\) và \(\frac{1}{10^{4024}}\)

Bài 1 : Thực hiện phép tính

(1) D = \(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{16}\left(1+2+...+16\right)\)

(2) M =\(\frac{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{99}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)

Bài 2 : Tìm x biết

(1) \(x-\left\{x-\left[x-\left(-x+1\right)\right]\right\}=1\)

(2) \(\left[\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}\right]\cdot x=\frac{2015}{1}+\frac{2014}{2}+...+\frac{1}{2015}\)

(3) \(\frac{x}{\left(a+5\right)\left(4-a\right)}=\frac{1}{a+5}+\frac{1}{4-a}\)

(4) \(\frac{x+2}{11}+\frac{x+2}{12}+\frac{x+2}{13}=\frac{x+2}{14}+\frac{x+2}{15}\)

(5) \(\frac{x+1}{2015}+\frac{x+2}{2014}+\frac{x+3}{2013}+\frac{x+4}{2012}+4=0\)

Bài 3 : 

(1) Cho : A =\(\frac{9}{1}+\frac{8}{2}+\frac{7}{3}+...+\frac{1}{9}\); B =\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}\)

CMR : \(\frac{A}{B}\)Là 1 số nguyên

(2) Cho : D =\(\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+...+\frac{1}{2000}\)CMR : \(D< \frac{3}{4}\)

Bài 4 : Ký hiệu [x] là số nguyên lớn nhất không vượt quá x , gọi là phần nguyên của x.

VD : [1.5] =1 ; [3] =3 ; [-3.5] = -4

(1) Tính :\(\left[\frac{100}{3}\right]+\left[\frac{100}{3^2}\right]+\left[\frac{100}{3^3}\right]+\left[\frac{100}{3^4}\right]\)

(2) So sánh : A =\(\left[X\right]+\left[X+\frac{1}{5}\right]+\left[X+\frac{2}{5}\right]+\left[X+\frac{3}{5}\right]+\left[X+\frac{4}{5}\right]\)và B = [5x]. Biết x=3.7

A/ \(\left(1-\frac{2}{3}\right)^2\)+ I \(\frac{-5}{6}\)I + \(\left(\frac{_{-7}}{12}\right)\)

B/ \(\left(\frac{3}{7}\right)^0\). \(1^{20}\) + \(\frac{7}{9}:\left(\frac{2}{3}\right)^2\) - \(\sqrt{\frac{16}{25}}\)

C/ \(\frac{3^{186}.25^{50}}{15^{100}.27^{29}}\)
 

1. Tìm x, biết:

a) \(\frac{x}{-15}=\frac{-60}{x}\)       

b) \(\frac{-2}{x}=\frac{-x}{\frac{8}{25}}\)

c) \(3,8:\left(2x\right)=\frac{1}{4}:2\frac{2}{3}\)

d) \(1\frac{1}{3}:0,8=\frac{2}{3}:\left(0,1x\right)\)

2. Tìm x,y, biết:  \(\frac{x}{12}=\frac{y}{24}\)và x.y=98

3. Tìm x, biết:

a) \(\left(2x+3\right)^2=\frac{9}{121}\)

b) \(\left(3x-1\right)^3=\frac{-8}{27}\)

Tìm x biết:
a)\(\left(2x+3\right)^2=25\) b)\(\left(x+2\right)^2=\frac{1}{2}-\frac{1}{3}\)
c)\(\left(x-1\right)^{x+2}=\left(x-1\right)^2\)  d)\(5^x+5^{x+2}=650\)
e)\(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)
f)\(\left(2x-1\right)^2-5=20\)

Tìm x biết:

1)  \(8^{x+3}+2^{3x}-3.2^{x+4}.4^{x+1}=321\)

2)  \(\left|x+1\right|+2.\left|x-2\right|=6\)

3) \(\left|3-2x\right|=x+1\)

4) \(\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}\right).x=\frac{2013}{1}+\frac{2012}{2}+...+\frac{2}{2012}+\frac{1}{2013}\)

Tìm giá trị nhỏ nhất của các biểu thức sau:

\(A=\left|4x-\frac{7}{3}\right|+2004\)

\(B=\left|x-1\right|+\left|x-2\right|+\left|x-3\right|+\left|x-4\right|\)

\(C=\left|x-4\right|+\left|x-28\right|+\left|x-60\right|\)

\(D=\left|x\right|+\left|x-1\right|+\left|x-2\right|+\left|x-3\right|+...+\left|x-99\right|\)

\(E=\left|x\right|+\left|x-1\right|+\left|x-2\right|+\left|x-3\right|+...+\left|x-2004\right|\)

P/s: Mong mọi người giúp đỡ mình ạ, được câu nào hay câu đó. Mình xin trân trọng cảm ơn!

Question 1:
Fill the suitable number in the following blank?
.\(343=\)_____\(3\)

Question 2:
The positive value of  such that  \(\left|2x-3\right|+7=16\) is _______

Question 3:
Given a function \(g\left(x\right)=2\sqrt{x-7}\) . Find the value of \(g\left(11\right)\)?
Answer: The value of \(g\left(11\right)\) is ._________

Question 4:
Find the value of  such that \(0,008=\left(0,2\right)^x\).
Answer: . \(x=\)_________

Question 5:
Given a function\(g\left(x\right)=\frac{2}{3-x}\) . Find the value of .\(g\left(1\right)+g\left(2\right)\)
Answer: The value of \(g\left(1\right)+g\left(2\right)\) is ._______

Question 6:
Suppose that \(\frac{7y-x}{2x+y}=\frac{1}{3}\) then the ratio of  \(x\) to  \(y\)  is .________

Question 7:
If \(x\) is directly proportional to \(y\) with the scaling factor is 8, \(z\)  is directly proportional to \(x\) with the scaling factor is 4.
Then \(z\)  is directly proportional to \(y\) with the scaling factor is______ .

Question 8:
The maximum value of \(A=\frac{6}{2.\left(x-3\right)^2+3}\) is .______

Question 10:
Suppose that\(\frac{7-3x}{5}=\frac{y+4}{3}=\frac{6x-y}{5}\) . Find the ratio of \(y\) to \(x\)
Answer: The ratio of \(y\) to \(x\) is .______________-
(write your answer by decimal in simplest form)