5/3 - x = 1/1×2 + 1/2×3 + 1/3×4+. . .+1/38×39
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NN
3
VC
Vũ Cao Minh⁀ᶦᵈᵒᶫ ( ✎﹏IDΣΛ亗 )
CTV
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30 tháng 1 2020
a) \(A=2^{100}-2^{99}-2^{98}-...-2^2-2^1\)( Có 2 câu nên mình tính nhanh luôn nhé )
\(\Leftrightarrow A=2^{100}-\left(2^1+2^2+2^3+...+2^{98}+2^{99}\right)\)
\(A=2^{100}-\left(2^{100}-2^1\right)=2^{100}-2^{100}+2=2\)
b) \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{36.37.38}+\frac{1}{37.38.39}\)
\(=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{38-36}{36.37.38}+\frac{39-37}{37.38.39}\)
\(=\left(\frac{3}{1.2.3}-\frac{1}{1.2.3}\right)+\left(\frac{4}{2.3.4}-\frac{2}{2.3.4}\right)+...+\left(\frac{39}{37.38.39}-\frac{37}{37.38.39}\right)\)
\(=\left(\frac{1}{2}-\frac{2}{3}\right)+\left(\frac{2}{3}-\frac{3}{4}\right)+\left(\frac{3}{4}-\frac{4}{5}\right)+...+\left(\frac{1}{37.38}-\frac{1}{38.39}\right)\)
\(=\frac{1}{2}-\frac{2}{3}+\frac{2}{3}-\frac{3}{4}+\frac{3}{4}-\frac{4}{5}+...+\frac{1}{37.38}-\frac{1}{38.39}\)
\(=\frac{1}{2}-\frac{1}{38.39}=\frac{741}{1482}-\frac{1}{1482}=\frac{740}{1482}=\frac{370}{741}\)
TN
1
TM
7 tháng 5 2018
\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{37\cdot38\cdot39}\)
\(=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{37\cdot38}-\frac{1}{38\cdot39}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{38\cdot39}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{1482}\right)\)
\(=\frac{1}{2}\cdot\frac{370}{741}\)
\(=\frac{185}{741}\)
5 tháng 4 2017
\(S=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{37.38.39}\)
\(\Rightarrow S=\dfrac{1}{2}\left(\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+...+\dfrac{2}{37.38.39}\right)\)
\(\Rightarrow S=\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{37.38}-\dfrac{1}{38.39}\right)\)
\(\Rightarrow S=\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{38.39}\right)\)
\(\Rightarrow S=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{38.39}\right)\)
\(\Rightarrow S=\dfrac{1}{4}-\dfrac{1}{38.2.39}\)
Vậy...
5 tháng 4 2017
\(S=\dfrac{1}{2}.\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+..+\dfrac{1}{37.38}-\dfrac{1}{38.39}\right)\)
\(S=\dfrac{1}{2}.\left(\dfrac{1}{1.2}-\dfrac{1}{38.39}\right)\)
\(S=\dfrac{185}{741}\)
mk nghĩ vậy bạn ạ, nếu sai đừng trách mk nha bạn
31 tháng 1 2022
1: \(=\left(217-213+186\right)+\left(-14-49+54\right)\)
\(=190-9=181\)
2: \(=-38\cdot25+38\cdot4-25\cdot4+25\cdot38\)
\(=13\cdot4=52\)
3: \(=-39\cdot5+39\cdot99+99\cdot10-99\cdot39\)
\(=-195+990=795\)
4: =(1+3-5-7)+(9+11-13-15)+...+(393+395-397-399)
=(-8)+(-8)+...+(-8)
=-800
\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+....+\dfrac{1}{38.39}=\dfrac{5}{3}-x\)
=> \(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+......+\dfrac{1}{38}-\dfrac{1}{39}=\dfrac{5}{3}-x\)
=> \(1-\dfrac{1}{39}=\dfrac{5}{3}-x\)
=> \(\dfrac{39}{39}-\dfrac{1}{39}=\dfrac{65}{39}-\dfrac{39x}{39}\)
=> 39-1=65-39x
=> 38=65-39x
=> 39x=-38+65
=> 39x=27
=> x=\(\dfrac{9}{13}\)
vậy x= \(\dfrac{9}{13}\)