Tính S=1*2+2*3+3*4+.....+37*38+38*39
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Tính S= 1/ 1*2*3+1/ 2*3*4+1/ 3*4*5+...+1/ 37*38*39
\(S=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{37.38.39}\)
\(\Rightarrow S=\dfrac{1}{2}\left(\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+...+\dfrac{2}{37.38.39}\right)\)
\(\Rightarrow S=\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{37.38}-\dfrac{1}{38.39}\right)\)
\(\Rightarrow S=\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{38.39}\right)\)
\(\Rightarrow S=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{38.39}\right)\)
\(\Rightarrow S=\dfrac{1}{4}-\dfrac{1}{38.2.39}\)
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\(S=\dfrac{1}{2}.\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+..+\dfrac{1}{37.38}-\dfrac{1}{38.39}\right)\)
\(S=\dfrac{1}{2}.\left(\dfrac{1}{1.2}-\dfrac{1}{38.39}\right)\)
\(S=\dfrac{185}{741}\)
mk nghĩ vậy bạn ạ, nếu sai đừng trách mk nha bạn
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tinh s=1/1*2*3+1/02*3*4+1/3*4*5+...+1/37*38*39
a=1/1*2*3+1/2*3*4+1/3*4*5+1/37*38*39.Tính a
S=1/2+1/3+...+1/38+1/39,P=1/39+2/38+...+38/2+39/1 tính S/P
2/2*3*4+2/3*4*5+...+2/37*38*39+2/38*39*40
2/2*3*4+2/3*4*5+...+2/37*38*39+2/38*39*40
Tính nhanh:
1/1×2×3 + 1/2×3×4 + 1/3×4×5 + ... + 1/37×38×39
\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{37\cdot38\cdot39}\)
\(=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{37\cdot38}-\frac{1}{38\cdot39}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{38\cdot39}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{1482}\right)\)
\(=\frac{1}{2}\cdot\frac{370}{741}\)
\(=\frac{185}{741}\)
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a ) A=2^100 -2^99 -2^98 -...-2^2-2-1
b) 1/1*2*3 +2*3*4 +1/3*4*5+...+1/36*37*38 +1/37*38*39
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) \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{36.37.38}+\frac{1}{37.38.39}\)
\(=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{38-36}{36.37.38}+\frac{39-37}{37.38.39}\)
\(=\left(\frac{3}{1.2.3}-\frac{1}{1.2.3}\right)+\left(\frac{4}{2.3.4}-\frac{2}{2.3.4}\right)+...+\left(\frac{39}{37.38.39}-\frac{37}{37.38.39}\right)\)
\(=\left(\frac{1}{2}-\frac{2}{3}\right)+\left(\frac{2}{3}-\frac{3}{4}\right)+\left(\frac{3}{4}-\frac{4}{5}\right)+...+\left(\frac{1}{37.38}-\frac{1}{38.39}\right)\)
\(=\frac{1}{2}-\frac{2}{3}+\frac{2}{3}-\frac{3}{4}+\frac{3}{4}-\frac{4}{5}+...+\frac{1}{37.38}-\frac{1}{38.39}\)
\(=\frac{1}{2}-\frac{1}{38.39}=\frac{741}{1482}-\frac{1}{1482}=\frac{740}{1482}=\frac{370}{741}\)
2 / 2 * 3 * 4 + .....+ 2 / 37 * 38 * 39 + 2 / 38 * 39 * 40