35 . 99 + 35 + 25 . 63 + 25 . 63 + 25 . 38 - 25 Tính nhanh
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\(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{25}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)
\(=\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+\dfrac{2}{9\cdot11}+\dfrac{2}{11\cdot13}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)
\(=\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-...+\dfrac{1}{11}-\dfrac{1}{13}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)
\(=\left(1-\dfrac{1}{3}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)
\(=\dfrac{2}{3}\cdot\dfrac{1}{2}+\dfrac{1}{25}\)
\(=\dfrac{1}{3}+\dfrac{1}{25}\)
\(=\dfrac{28}{75}\)
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24 . 25 + ( 4 . 6 ) . 37 + 24 . 38
24 . 25 + 24 . 37 + 24 . 38
24 . ( 25 + 37 + 38 )
24 . 100
2400
24 . 25 + 4 . 37 . 6 +24 . 38
= 24 . 25 + 24 . 37 + 24 . 38
= 24 . ( 25 + 38 + 37 )
= 24 . 100 = 2400
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a, =46x(-217+117) =46x(-100)=-4600
b, =-25x(78-28)=-25x50=-1250
c,=35(-63-23)=35x(-86)=3010
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\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+....+\frac{2}{575}+\frac{2}{675}\)
\(=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{23\times25}+\frac{2}{25\times27}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{23}-\frac{1}{25}+\frac{1}{25}-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}=\frac{8}{27}\)
Vậy ....
\(\frac{2}{15}+\frac{2}{35}+\frac{2}{69}+........+\frac{2}{575}+\frac{2}{675}\)
\(=\frac{2}{3\times5}+\frac{2}{5\times7}+........+\frac{2}{23\times25}+\frac{2}{25\times27}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.......+\frac{1}{23}-\frac{1}{25}+\frac{1}{25}-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}\)
\(=\frac{8}{27}\)
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=(1-1/2)(1+1/2)*...*(1+1/10)(1-1/10)
=1/2*2/3*...*9/10*3/2*4/3*...*11/10
=1/10*11/2
=11/20
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\(=\frac{25}{35}\times\frac{18}{12}\times\frac{63}{24}\)
\(=\frac{5}{7}\times\frac{3}{2}\times\frac{21}{8}\)
\(=\frac{5\times3\times3}{1\times2\times8}\)
\(=\frac{45}{16}\)
\(35\cdot99+35+25\cdot63+25\cdot63+25\cdot38-25\)
\(=35\cdot\left(99+1\right)+25\cdot\left(63+63+38-1\right)\)
\(=35\cdot100+25\cdot163\)
\(=3500+4075\)
\(=7575\)
\(35\cdot99+35+25\cdot63+25\cdot63+25\cdot38-25\)
\(=35(99+1)+25(63+63+38-1)\)
\(=35\cdot100+25\cdot163\)
\(=3500+4075\)
\(=7575\)