ta có : \(S=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{2017.2018}\)
\(\Leftrightarrow S=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{2017}-\dfrac{1}{2018}\)
\(\Leftrightarrow S=\dfrac{1}{2}-\dfrac{1}{2018}=\dfrac{504}{1009}\)
1,Chứng minh rằng:
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{1990^2}< \dfrac{3}{4}\)
2,Chứng minh rằng:
\(1< \dfrac{x}{x+y}+\dfrac{y}{y+z}+\dfrac{z}{z+x}< 2\)
Tìm x:
a/\(\dfrac{x-1}{x+5}=\dfrac{6}{7}\)
b/\(\dfrac{x^2}{-6}=-\dfrac{24}{25}\)
c/\(\dfrac{x+4}{20}=\dfrac{5}{x+4}\)
d/\(2,5:4x=0,5:0,2\)
e/\(\dfrac{1}{5}x:3=\dfrac{2}{3}:0,25\)
g/\(1,25:0,8=\dfrac{3}{8}:0,2x\)
f/\(-3:\left(-2\dfrac{1}{4}\right)=\dfrac{3}{4}:\left(-6x\right)\)
h/\(3:\dfrac{2}{5}x=1:0,01\)
j/\(2:1\dfrac{1}{4}=\dfrac{1}{2}:2x\)
l/\(\dfrac{4}{x-1}=\dfrac{x-1}{9}\)
\(\dfrac{x}{y+z+1}=\dfrac{y}{x+z+2}=\dfrac{z}{x+y-3}=x+y+z\)
Tìm a,b,c biết:
\(\dfrac{1}{2}a=\dfrac{2}{3}b\) = \(\dfrac{3}{4}c\)
1.viết tất cả các tỉ lệ thức từ các đẳng thức sau
a) 3*5=-1*-15
b) 4*9=-3*-12
c)3*b=7*c
d) a*x=b*y
2.tìm x
a) \(\dfrac{x-1}{4}=\dfrac{9}{x-1}\)
b)\(\dfrac{x+2}{5}=\dfrac{20}{x+2}\)
1) Tính :
a)(1000-1^3)(1000-2^3)(1000-3^3)....(1000-2^2018)
2)Tìm x , biết :
\(\dfrac{27}{3^x}\)=3
3) Tìm x, y biết :
a)\(x^2\)+\(\left(y-\dfrac{1}{10}\right)^{2018}\)=0
b)\(\left(\dfrac{1}{2}x-5\right)^{20}\)+\(\left(y^2-\dfrac{1}{4}\right)^{10}\)\(\le\)0
-12/13x-5=\(6\dfrac{1}{13}\)
So sánh:
A= \(\dfrac{1.3.5+2.6.10+4.12.20}{1.5.7+2.10.12+4.20.28}\)với\(\dfrac{3}{8}\)
x\(^2\)+(y-\(\dfrac{1}{10}\))\(^4\)=0