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ta có :
\(A=\frac{1}{2^2}+\frac{1}{3^2}+..+\frac{1}{n^2}< \frac{1}{1.2}+\frac{1}{2.3}+..+\frac{1}{\left(n-1\right)n}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+..+\frac{1}{n-1}-\frac{1}{n}=1-\frac{1}{n}< 1\) Vậy A<1
b. \(4B=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+..+\frac{1}{n^2}=1+A< 2\Rightarrow B< 0.5\)
trtrfdretrrfgt.........................................................
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1) \(2x - \frac{3}{4}= \left ( + \frac{2}{3} \right )\)
\(2x = \frac{2}{3}+ \frac{3}{4}\)
\(2x = \frac{17}{12}\)
\(x = \frac{17}{12}: 2\)
x = \(\frac{17}{24}\)
Vậy ...........
2) x5 : x3 = \(\frac{1}{16}\)
\(x^{2}= \frac{1}{16}\)
=> \(x= \frac{1}{14}\) hoặc \(x= - \frac{1}{14}\)
Vậy ........
3) \(\left | x + \frac{1}{3} \right | - 2 = - 1\)
\(\left | x + \frac{1}{3} \right | = 1\)
* \(x + \frac{1}{3} = 1\)
\(x = 1 - \frac{1}{3}\)
\(x = \frac{2}{3}\)
* \(x + \frac{1}{3} = - 1\)
\(x =- 1 - \frac{1}{3}\)
\(x = - \frac{4}{3}\)
Vậy ...........hoặc..............
4) \(\frac{2}{9}x\left (x - 3\tfrac{7}{8} \right )= 0\)
\(\frac{2}{9}x\left (x - \frac{31}{8} \right )= 0\)
<=> \(\begin{bmatrix} \frac{2}{9}x = 0 & & \\ x - \frac{31}{8}= 0 & & \end{bmatrix}\)
\(\Leftrightarrow \begin{bmatrix} x = 0 & & \\ x = \frac{31}{8} & & \end{bmatrix}\)
pn bỏ dấu ngoặc bên phải nhé
Vậy ...............hoặc............
Chúc pn học tốt
và a + b + c = 350
a/ Áp dụng t.c dãy tỉ số bằng nhau ta có :
\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{5}=\dfrac{a+b+c}{2+3+5}=\dfrac{350}{10}=35\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{a}{2}=35\\\dfrac{b}{3}=35\\\dfrac{c}{5}=35\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a=70\\b=105\\c=175\end{matrix}\right.\)
Vậy .....
b/ \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{4}{9}\)
\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2=\left(\dfrac{2}{3}\right)^2=\left(-\dfrac{2}{3}\right)^2\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{2}{3}\\x+\dfrac{1}{2}=-\dfrac{2}{3}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{6}\\x=-\dfrac{7}{6}\end{matrix}\right.\)
Vậy ..
2. Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{5}=\dfrac{a+b+c}{2+3+5}=\dfrac{350}{10}=35\\ \Rightarrow\left\{{}\begin{matrix}a=35\cdot2=70\\b=35\cdot3=105\\c=35\cdot5=175\end{matrix}\right.\)
3.
\(\left(x+\dfrac{1}{2}\right)^2=\dfrac{4}{9}\\ \Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{2}{3}\\x+\dfrac{1}{2}=-\dfrac{2}{3}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}-\dfrac{1}{2}\\x=\dfrac{-2}{3}-\dfrac{1}{2}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{6}\\x=\dfrac{-7}{6}\end{matrix}\right.\)
Bài 2:
Với x,y,z,t là số tự nhiên khác 0
Có \(\dfrac{x}{x+y+z+t}< \dfrac{x}{x+y+z}< \dfrac{x}{x+y}\)
\(\dfrac{y}{x+y+z+t}< \dfrac{y}{x+y+t}< \dfrac{y}{x+y}\)
\(\dfrac{z}{x+y+z+t}< \dfrac{z}{y+z+t}< \dfrac{z}{z+t}\)
\(\dfrac{t}{x+y+z+t}< \dfrac{t}{x+z+t}< \dfrac{t}{z+t}\)
Cộng vế với vế \(\Rightarrow1< M< \dfrac{x+y}{x+y}+\dfrac{z+t}{z+t}=2\)
=> M không là số tự nhiên.
Bài 1:
Ta có:
\(B=\dfrac{2008}{1}+\dfrac{2007}{2}+\dfrac{2006}{3}+...+\dfrac{2}{2007}+\dfrac{1}{2008}\)
\(B=\left(1+\dfrac{2007}{2}\right)+\left(1+\dfrac{2006}{3}\right)+...+\left(1+\dfrac{2}{2007}\right)+\left(1+\dfrac{1}{2008}\right)+1\)
\(B=\dfrac{2009}{2}+\dfrac{2009}{3}+...+\dfrac{2009}{2007}+\dfrac{2009}{2008}+\dfrac{2009}{2009}\)
\(B=2009.\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2007}+\dfrac{1}{2008}+\dfrac{1}{2009}\right)\)
\(\Rightarrow\dfrac{A}{B}=\dfrac{2009.\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2007}+\dfrac{1}{2008}+\dfrac{1}{2009}\right)}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2007}+\dfrac{1}{2008}+\dfrac{1}{2009}}=2009\)