Bài 1.

A=\(\frac{1}{1}\)x\(\frac{1}{2}\)x\(\frac{1}{2}\)x\(\frac{1}{3}\)x\(\frac{1}{3}\)x\(\frac{1}{4}\)x\(\frac{1}{4}\)x\(\frac{1}{5}\)x\(\frac{1}{5}\)x\(\frac{1}{6}\)

Bài 2.

B=\(\frac{1}{1x2}\)+\(\frac{1}{2x3}\)+\(\frac{1}{3x4}\)+\(\frac{1}{4x5}\)+\(\frac{1}{5x6}\)

Bài 3.

B=\(\frac{2}{1x2}\)+\(\frac{2}{2x3}\)+\(\frac{2}{3x4}\)+\(\frac{2}{4x5}\)+\(\frac{2}{5x6}\)

Bài 4.

C=\(\frac{2}{1x3}\)+\(\frac{2}{3x5}\)+\(\frac{2}{5x7}\)+\(\frac{2}{7x9}\)+\(\frac{2}{9x11}\)

Bài 5.

C=\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{90}+\frac{1}{110}\)

Bài 6.Tính bằng cách thuận tiện nhất.

a.(792,81 x 025 + 792,81 x 0,75) x (11 x 9 - 900 x 0,1 - 9).

b.\(\frac{7,2:2x57,2+2,86x2x64}{4+4+8+12+20+....+220}\)

c.\(\frac{2003x14+1998+2001x2002}{2002+2002x503+504x2002}\)

d.\(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{28}\)

đ.3,54 x 73 + 0,23 x 25 + 3,54 x 27 + 0,17 x 25

e.\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\)

g.\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)\)

Tìm x biết :

4,\(\frac{\left(-3\right)^x}{81}=-27\)

5,\(1\frac{1}{2}.x-4=0,5\)

6,\(2^{x-1}=16\)

7,\(\left(x-1\right)^2=25\)

8,\(|2x-1|=5\)

9,\(0,2-|4,2-2x|=0\)

11,\(1\frac{2}{3}:\frac{x}{4}=6:0,3\)

12,\(2\frac{2}{3}:x=1\frac{7}{9}:2\frac{2}{3}\)

bài 1:

a)\(\frac{1}{4}\)-\(\frac{1}{3}\)x =\(\frac{2}{5}\)-\(\frac{3}{2}\)x

b)5.x\(^{^{x-2}}\)+3.2\(^{^x}\)=2\(^{^{2016}}\).17

c) (\(\frac{1}{2}\)-\(\frac{1}{6}\)).3\(^{^{x+4}}\)-4.3\(^{^x}\)=3\(^{^{16}}\)-4.3\(^{^{13}}\)

Câu 3 : Giác các bất phương trình sau

a , \(\frac{2}{x-1}< \frac{5}{2x-1}\)

b , \(\frac{1}{x+1}< \frac{1}{\left(x-1\right)^2}\)

c , \(\frac{1}{x}+\frac{2}{x+4}< \frac{3}{x+3}\)

d , \(\frac{x^2-3x+1}{x^2-1}< 1\)

e , \(\frac{3}{2-x}< 1\)

f , \(\frac{x^2+x-3}{x^2-4}\ge1\)

g , \(\frac{1}{x-1}+\frac{1}{x+2}>\frac{1}{x-2}\)

h , \(\frac{3x-4}{x-2}>1\)

i , \(\frac{2x-5}{2-x}\ge-1\)

k , \(\frac{-4}{3x+1}< \frac{3}{2-x}\)

l , \(\frac{2}{x-3}+\frac{4}{x+3}\le\frac{5x-1}{x^2-9}\)

m , \(\frac{x+1}{18}+\frac{-2x+1}{9}\le1\)

Bài 2 : Giải các bất phương trình sau :

11 , \(\left(2x-7\right)\left(4-5x\right)\ge0\)

12 , \(x^2-x-20>2\left(x-11\right)\)

13 , \(3x\left(2x+7\right)\left(9-3x\right)\ge0\)

14 , \(x^3+8x^2+17x+10< 0\)

15 , \(x^3+6x^2+11x+6>0\)

16 , \(\frac{\left(2x-5\right)\left(x+2\right)}{-4x+3}>0\)

17 , \(\frac{x-3}{x+1}>\frac{x+5}{x-2}\)

18 , \(\frac{x-3}{x+5}< \frac{1-2x}{x-3}\)

19 , \(\frac{3x-4}{x-2}>1\)

20 , \(\frac{2x-5}{2-x}\ge-1\)

Câu 2 : Xét dấu các biểu thức sau :

A = \(\frac{4-3x}{2x+1}\)

B = \(1-\frac{2-x}{3x-2}\)

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

D = \(\frac{x\left(x-3\right)^2}{\left(x-5\right)\left(1-x\right)}\)

E = \(-x^2+x+6\)

F = \(2x^2-\left(2+\sqrt{3}\right)x+\sqrt{3}\)

G = \(\left(3x-1\right)\left(x+2\right)\)

H = \(\frac{2-3x}{5x-1}\)

K = \(\left(-x+1\right)\left(x+2\right)\left(3x+1\right)\)

L = \(2-\frac{2+x}{3x-2}\)

M = \(9x^2-1\)

N = \(-x^3+7x-6\)

O = \(x^3+x^2-5x+3\)

P = \(x^2-x-2\sqrt{2}\)

Q = \(\frac{1}{3-x}-\frac{1}{3+x}\)

R = \(\frac{x^2-6x+8}{x^2+8x-9}\)

S= \(\frac{x^2+4x+4}{x^4-2x^2}\)

T = \(\frac{\left|x+1\right|-1}{x^2+x+1}\)

Tìm x biết:

a/ (152\(\frac{2}{4}\) - 148\(\frac{3}{8}\)) : 0,2= x:0,3

b/ (85\(\frac{7}{30}\) -83\(\frac{5}{18}\) ) : 2\(\frac{2}{3}\) = 0,01.x:4

c/ \(\frac{x-1}{x+5}=\frac{6}{7}\)

d/ \(\frac{x}{19}=\frac{y}{21}và2x-y=34\)

e/ \(\frac{x}{15}=\frac{y}{20}=\frac{z}{28}và3x+2y-2z=186\)

bài 1: tính các giá trị lượng giác còn lại biết:

1) sin x=\(\frac{3}{5}\)với 0<x<\(\frac{\pi}{2}\)

2) cos x=\(\frac{5}{13}\)với\(\frac{3\pi}{2}\)<x<2π

3) cos x=\(-\frac{2}{5}với\frac{\pi}{2}< x< \pi\)

4) tan x=-2 với \(\frac{\pi}{2}< x< \pi\)

5) sin x=\(-\frac{1}{3}với\) \(\pi< x< \frac{3\pi}{2}\)

6) cot x=\(\frac{1}{2}với\) 0<x<\(\frac{\pi}{2}\)