Tính: C=1 + 1/2 x 2.3/2 +1/3 x 3.4/2 +1/4 x 4.5/2 +.............+1/20 x 20.21/2
Những câu hỏi liên quan
1+2.(1/2.3+1/3.4+1/4.5+...+1/x.(x+1)=3/2
1+2.( 1/2-1/3+1/3-1/4+....+1/(x-1)-1/x+1)=3/2
1+2.(1/2-1/x+1)=3/2
1-2/x+1=3/2-1
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text{Tìm x, biết:}a) x-dfrac{2}{3.5}-dfrac{2}{5.7}-dfrac{2}{7.9}-dfrac{2}{9.11}-dfrac{2}{11.13}-dfrac{2}{13.15}dfrac{2}{5}b) dfrac{1}{2.3}.x+dfrac{1}{3.4}.x+dfrac{1}{4.5}.x+...+dfrac{1}{49.50}.x1c) x-dfrac{20}{11.3}-dfrac{20}{13.15}-...-dfrac{53}{55}dfrac{3}{11}d) x+dfrac{4}{5.9}+dfrac{4}{9.13}+...+dfrac{4}{41.45}dfrac{-37}{45}e) left(dfrac{11}{12}.dfrac{11}{2.23}.dfrac{11}{23.34}...dfrac{11}{89.100}right).xdfrac{5}{3}f) left(dfrac{2}{11.13}.dfrac{2}{13.15}.dfrac{2}{15.17}...dfrac{2}{19.21}right...
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\(\text{Tìm x, biết:}\)
\(a\)) \(x-\dfrac{2}{3.5}-\dfrac{2}{5.7}-\dfrac{2}{7.9}-\dfrac{2}{9.11}-\dfrac{2}{11.13}-\dfrac{2}{13.15}=\dfrac{2}{5}\)
\(b\)) \(\dfrac{1}{2.3}.x+\dfrac{1}{3.4}.x+\dfrac{1}{4.5}.x+...+\dfrac{1}{49.50}.x=1\)
\(c\)) \(x-\dfrac{20}{11.3}-\dfrac{20}{13.15}-...-\dfrac{53}{55}=\dfrac{3}{11}\)
\(d\)) \(x+\dfrac{4}{5.9}+\dfrac{4}{9.13}+...+\dfrac{4}{41.45}=\dfrac{-37}{45}\)
\(e\)) \(\left(\dfrac{11}{12}.\dfrac{11}{2.23}.\dfrac{11}{23.34}...\dfrac{11}{89.100}\right).x=\dfrac{5}{3}\)
\(f\)) \(\left(\dfrac{2}{11.13}.\dfrac{2}{13.15}.\dfrac{2}{15.17}...\dfrac{2}{19.21}\right)-x+4+\dfrac{221}{231}=\dfrac{7}{3}\)
d) Ta có: \(x+\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+...+\dfrac{4}{41\cdot45}=\dfrac{-37}{45}\)
\(\Leftrightarrow x+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{41}-\dfrac{1}{45}=\dfrac{-37}{45}\)
\(\Leftrightarrow x+\dfrac{1}{5}-\dfrac{1}{45}=\dfrac{-37}{45}\)
\(\Leftrightarrow x=\dfrac{-37}{45}+\dfrac{1}{45}-\dfrac{1}{5}=\dfrac{-36}{45}-\dfrac{1}{5}=\dfrac{-4}{5}-\dfrac{1}{5}=-1\)
Vậy: x=-1
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1.Tìm x:
\(\frac{x}{2}\)+\(\frac{x}{3}=\frac{1}{4}\)
2.Tính
M=\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{2008.2009}\)
Bài 2:
\(M=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2008.2009}\)
\(\Rightarrow M=\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{2009-2008}{2008.2009}\)
\(\Rightarrow M=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2008}-\frac{1}{2009}=\frac{1}{2}-\frac{1}{2009}\)
Bài 1:
Ta có: \(\frac{x}{2}+\frac{x}{3}=x\left(\frac{1}{2}+\frac{1}{3}\right)=\frac{5}{6}x=\frac{1}{4}\Rightarrow x=\frac{3}{10}\)
tính: A=1/4+1/12+1/24+....+1/220
B=(1-1/4)x(1-1/9)x(1-1/16)x...x(1-1/100)
C=(1-2/2.3)x(1-2/3.4)x(1-2/4.5)x....x(1-2/99.100)
cả . ,x đều là nhân
(1- 2/2.3) x (1- 2/3.4) x (1- 2/4.5) x...x (1- 2/98.99)
Giúp mình với
Tìm x biết
a,(3x-1).1/2x+5=0
b,-5.(x+1/5)-1/2.(x+3/5)=-x+1/5
c,2|1/2x-1/3|-3/2=1/4
d,|20/9-x|=1/12+1/20+1/30+1/42+1/56+1/72
e,1/2.3.x+1/3.4.x+1/4.5.x+...+1/49.50.x=1
MÌNH ĐANG CẦN GẤP.CẢM ƠN CÁC BẠN ĐÃ GIÚP!!!!
c, Ta có: \(2.|\dfrac{1}{2}x - \dfrac{1}{3}| - \dfrac{3}{2} = \dfrac{1}{4}\)
\(\Rightarrow\) \(2.|\dfrac{1}{2}x - \dfrac{1}{3}| = \dfrac{7}{4}\)
\(\Rightarrow\) \(|\dfrac{1}{2}x - \dfrac{1}{3}| = \dfrac{7}{8}\)
\(\Rightarrow\) \(\left[{}\begin{matrix}\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{7}{8}\\\dfrac{1}{2}x-\dfrac{1}{3}=-\dfrac{7}{8}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{1}{2}x=\dfrac{29}{24}\\\dfrac{1}{2}x=-\dfrac{13}{24}\end{matrix}\right.\)
\(\Rightarrow\) \(\left[{}\begin{matrix}x=\dfrac{29}{24}\\x=-\dfrac{13}{12}\end{matrix}\right.\)
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2/2.3+2/3.4+2/4.5+...+2/x(x+1)=2008/2010
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ĐKXĐ: \(x\ne0;x\ne-1\)
\(\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2008}{2010}\)
\(\Leftrightarrow2.\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+..+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2008}{2010}\)
\(\Leftrightarrow2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{2008}{2010}\)(Biết công thức này chứ?)
\(\Leftrightarrow2\left(\dfrac{1}{2}-\dfrac{1}{x+1}\right)=\dfrac{2008}{2010}\)
\(\Leftrightarrow1-\dfrac{2}{x+1}=\dfrac{2008}{2010}\)
\(\Leftrightarrow\dfrac{x-1}{x+1}=\dfrac{2008}{2010}\Leftrightarrow2010x-2010=2008x+2008\Leftrightarrow x=2009\left(tm\right)\)
Vậy x = 2009
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c,{[(20-2.3).5]-2.5} : 2 + (4.5) ²d,( 1 ² + 2 ² + 3 ² + ....+ 100 ²).(2^4 - 4^2)bài 2a, -2 x <5b, [31-(x+5)].11=121c,(x+1)³=27
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c) {[(20 - 2.3).5] - 2.5} : 2 + (4.5)²
= {(20 - 6).5] - 10} : 2 + 20²
= (14.5 - 10) : 2 + 400
= (70 - 10) : 2 + 400
= 60 : 2 + 400
= 30 + 400
= 430
d) (1² + 2² + 3² + ... + 100²) . (2⁴ - 4²)
= (1² + 2² + 3² + ... + 100²) . (16 - 16)
= (1² + 2² + 3² + ... + 100²) . 0
= 0
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Bài 2
a) -2x < 5
2x > 5
x > 5/2
b) [31 - (x + 5)].11 = 121
31 - (x + 5) = 121 : 11
31 - (x + 5) = 11
x + 5 = 31 - 11
x + 5 = 20
x = 20 - 5
x = 15
c) (x + 1)³ = 27
(x + 1)³ = 3³
x + 1 = 3
x = 3 - 1
x = 2
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Tìm X biết 2/2.3 + 2/3.4 + 2/4.5+...... +2/X(X+1) = 2007/2009