Tính
B=\(\frac{2.\text{ 4}.10+\text{ 4}.6.8+1\text{ 4}.16.20}{3.6.15+6.9.12+21.\text{ 24.30}}\)
Những câu hỏi liên quan
Rút gọn N= \(\dfrac{\text{2^19 x 27 ^3 - 15 . 4^9 . 9^4}}{\text{69 x 2^10 - 12^10}}\)
P = \(\dfrac{2.4.10+4.6.8+14.16.20}{3.6.15+6.9.12+21.24.30}\)
Giups mik trong thời gian ngắn nhất vs . cảm ơn
\(N=\dfrac{2^{19}\cdot3^9-3\cdot3^8\cdot5\cdot2^{18}}{3^9\cdot2^9\cdot2^{10}-2^{20}\cdot3^{10}}\)
\(=\dfrac{2^{18}\cdot3^9\cdot\left(2-5\right)}{3^9\cdot2^{19}\left(1-2\cdot3\right)}=\dfrac{1}{2}\cdot\dfrac{-3}{-5}=\dfrac{3}{10}\)
\(P=\dfrac{8\cdot10+8\cdot24+8\cdot560}{6\cdot45+6\cdot108+6\cdot120\cdot21}=\dfrac{8\left(10+24+560\right)}{6\left(45+108+120\cdot21\right)}=\dfrac{4}{3}\cdot\dfrac{2}{9}=\dfrac{8}{27}\)
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B = \(\dfrac{\text{2.4.10+4.6.8+14.16.20}}{3.6.15+6.9.12+21.24.30}\)
B= 2.4.10+4.6.8+14.16.20/3.6.15+6.9.12+21.24.30
B=2.[1.2.5 +2.3.4 +7.8.10]/3.[1 .2.5+2.3.4+7.8.10]
B=2/3
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B = \(\dfrac{2.4.10+4.6.8+14.16.20}{3.6.15+6.9.12+21.24.30}\)
B = \(\dfrac{2^3.\left(1.2.5+2.3.4+7.8.10\right)}{3^3.\left(1.2.5+2.3.4+7.8.10\right)}\)
B = \(\dfrac{2^3}{3^3}\)
B = \(\dfrac{8}{27}\)
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\(\frac{1\text{x}3\text{x}5+2\text{x}6\text{x}10+4\text{x}12\text{x}20+7\text{x}21\text{x}35}{1\text{x}5\text{x}7+2\text{x}10\text{x}14+4\text{x}20\text{x}28+7\text{x}35\text{x}49}\)
( hơi nhỏ xíu )
\(=\frac{1\cdot3\cdot5+2^3\cdot1\cdot3\cdot5+4^3\cdot1\cdot3\cdot5+7^3\cdot1\cdot3\cdot5}{1\cdot5\cdot7+2^3\cdot1\cdot5\cdot7+4^3\cdot1\cdot5\cdot7+7^3\cdot1\cdot5\cdot7}=\frac{1\cdot3\cdot5\cdot\left(1+2^3+4^3+7^3\right)}{1\cdot5\cdot7\cdot\left(1+2^3+4^3+7^3\right)}=\frac{3}{7}\)
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Xem thêm câu trả lời
\(\frac{2017}{1\times2\text{×}3}+\frac{2017}{2\text{×}3\text{×}4}+\frac{2017}{3\text{×}4\text{×}5}+..+\frac{2017}{19\text{×}20\text{×}21}\)
\(\frac{2017}{1.2.3}+\frac{2017}{2.3.4}+\frac{2017}{3.4.5}+...+\frac{2017}{19.20.21}\)
\(=2017\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{19.20.21}\right)\)
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\(=2017.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{19.20.21}\right)\)
\(=2017.\left(1-\frac{1}{2}-\frac{1}{3}-\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{4}\right)-...-\left(\frac{1}{19}-\frac{1}{20}-\frac{1}{21}\right)\right)\)
\(=2017.\left(1+\frac{1}{21}\right)\)phá ngoặc trước dấu trừ đổi dấu,rút gọn:
\(=2017.\frac{20}{21}=\frac{40340}{21}\)
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( Câu siêu khó dành cho học sinh đội tuyển Toán )( Giúp với )Bài 10 :b) frac{left(text{13}frac{text{1}}{text{4}}-text{2}frac{text{5}}{text{27}}-text{10}frac{text{5}}{text{6}}right).text{230}frac{text{1}}{text{25}}+text{46}frac{text{3}}{text{4}}}{left(text{1}frac{text{3}}{text{7}}+frac{text{10}}{text{3}}right):left(text{12}frac{text{1}}{text{3}}-text{14}frac{text{2}}{text{7}}right)}
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( Câu siêu khó dành cho học sinh đội tuyển Toán )
( Giúp với )
Bài 10 :
b) \(\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{2}\frac{\text{5}}{\text{27}}-\text{10}\frac{\text{5}}{\text{6}}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\left(\text{1}\frac{\text{3}}{\text{7}}+\frac{\text{10}}{\text{3}}\right):\left(\text{12}\frac{\text{1}}{\text{3}}-\text{14}\frac{\text{2}}{\text{7}}\right)}\)
\(\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{2}\frac{\text{5}}{\text{27}}-\text{10}\frac{\text{5}}{\text{6}}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\left(\text{1}\frac{\text{3}}{\text{7}}+\frac{\text{10}}{\text{3}}\right):\left(\text{12}\frac{\text{1}}{\text{3}}-\text{14}\frac{\text{2}}{\text{7}}\right)}=\frac{\left[\text{13}\frac{\text{1}}{\text{4}}-\left(\text{2}\frac{\text{5}}{\text{27}}+\text{10}\frac{\text{5}}{\text{6}}\right)\right].\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{100}}{\text{21}}:\frac{\text{-41}}{\text{21}}}\)
\(=\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{13}\frac{\text{1}}{54}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\frac{\text{25}}{\text{108}}.\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}\)
\(=\frac{\text{53}\frac{\text{1}}{\text{4}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\text{100}}{\frac{-\text{100}}{\text{41}}}=\text{-41}\)
Giải :
\(\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{2}\frac{\text{5}}{\text{27}}-\text{10}\frac{\text{5}}{\text{6}}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\left(\text{1}\frac{\text{3}}{\text{7}}+\frac{\text{10}}{\text{3}}\right):\left(\text{12}\frac{\text{1}}{\text{3}}-\text{14}\frac{\text{2}}{\text{7}}\right)}=\frac{\left[\text{13}\frac{\text{1}}{\text{4}}-\left(\text{2}\frac{\text{5}}{\text{27}}+\text{10}\frac{\text{5}}{\text{6}}\right)\right].\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{100}}{\text{21}}:\frac{\text{-41}}{\text{21}}}\)
\(=\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{13}\frac{\text{1}}{54}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\frac{\text{25}}{\text{108}}.\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}\)
\(=\frac{\text{53}\frac{\text{1}}{\text{4}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\text{100}}{\frac{-\text{100}}{\text{41}}}=\text{-41}\)
~~Học tốt~~
\(\text{Giải :}\)
\(\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{2}\frac{\text{5}}{\text{27}}-\text{10}\frac{\text{5}}{\text{6}}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\left(\text{1}\frac{\text{3}}{\text{7}}+\frac{\text{10}}{\text{3}}\right):\left(\text{12}\frac{\text{1}}{\text{3}}-\text{14}\frac{\text{2}}{\text{7}}\right)}=\frac{\left[\text{13}\frac{\text{1}}{\text{4}}-\left(\text{2}\frac{\text{5}}{\text{27}}+\text{10}\frac{\text{5}}{\text{6}}\right)\right].\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{100}}{\text{21}}:\frac{\text{-41}}{\text{21}}}\)
\(=\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{13}\frac{\text{1}}{54}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\frac{\text{25}}{\text{108}}.\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}\)
\(=\frac{\text{53}\frac{\text{1}}{\text{4}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\text{100}}{\frac{-\text{100}}{\text{41}}}=\text{-41}\)
\(\text{~~Học tốt~~}\)
Xem thêm câu trả lời
\(A=\frac{3}{\left(1\text{*}2\right)\text{*}\left(1\text{*}2\right)}+\frac{5}{\left(2\text{*}3\right)\text{*}\left(3\text{*}2\right)}+\frac{7}{\left(3\text{*}4\right)\text{*}\left(3\text{*}4\right)}+...............+\frac{19}{\left(9\text{*}10\right)\text{*}\left(10\text{*}9\right)}\)
theo bài ra ta có
n = 8a +7=31b +28
=> (n-7)/8 = a
b= (n-28)/31
a - 4b = (-n +679)/248 = (-n +183)/248 + 2
vì a ,4b nguyên nên a-4b nguyên => (-n +183)/248 nguyên
=> -n + 183 = 248d => n = 183 - 248d (vì n >0 => d<=0 và d nguyên )
=> n = 183 - 248d (với d là số nguyên <=0)
vì n có 3 chữ số lớn nhất => n<=999 => d>= -3 => d = -3
=> n = 927
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Thực hiện phép tínha) frac{text{x + 9}}{x^2 - 9}-frac{text{3}}{text{x^2 + 3x}}b) frac{text{3x + 5
}}{text{x^2 - 5x
}}+frac{text{ 25 - x
}}{text{25 - 5x
}}c) frac{text{3
}}{text{2x
}}+frac{text{3x - 3
}}{text{2x - 1
}}+frac{ 2x^2 + 1
}{text{4x^2 - 2x
}}d) frac{text{1}}{text{3x - 2 }}-frac{1}{text{3x + 2 }}- frac{text{3x - 6}}{text{4 - 9x^2}}e) frac{text{18 }}{text{(x - 3)(x^2 - 9) }}-frac{text{3 }}{text{x^2 - 6x + 9 }}-frac{text{x}}{text{x^2 - 9}}g) frac{text{x + 2 }}{text{x + 3 }}-frac{text{...
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Thực hiện phép tính
a) \(\frac{\text{x + 9}}{x^2 - 9}-\frac{\text{3}}{\text{x^2 + 3x}}\)
b) \(\frac{\text{3x + 5 }}{\text{x^2 - 5x }}+\frac{\text{ 25 - x }}{\text{25 - 5x }}\)
c) \(\frac{\text{3 }}{\text{2x }}+\frac{\text{3x - 3 }}{\text{2x - 1 }}+\frac{ 2x^2 + 1 }{\text{4x^2 - 2x }}\)
d) \(\frac{\text{1}}{\text{3x - 2 }}-\frac{1}{\text{3x + 2 }}- \frac{\text{3x - 6}}{\text{4 - 9x^2}}\)
e) \(\frac{\text{18 }}{\text{(x - 3)(x^2 - 9) }}-\frac{\text{3 }}{\text{x^2 - 6x + 9 }}-\frac{\text{x}}{\text{x^2 - 9}}\)
g) \(\frac{\text{x + 2 }}{\text{x + 3 }}-\frac{\text{5 }}{\text{x^2 + x - 6 }}+\frac{\text{1}}{\text{2 - x}}\)
h) \(\frac{\text{4x }}{\text{x + 2 }}-\frac{\text{3x }}{\text{x - 2 }}+\frac{\text{12x}}{\text{x^2 - 4}}\)
i) \(\frac{\text{ x + 1 }}{\text{ x - 1 }}-\frac{\text{ x - 1 }}{\text{ x + 1 }}-\frac{\text{4}}{\text{1 - x^2}}\)
k) \(\frac{\text{
3x + 21
}}{\text{
x^2 - 9
}}+\frac{\text{2 }}{\text{x + 3 }}-\frac{\text{3}}{\text{x - 3}}\)
Bài 4: Tính hợp lý
A=\(\frac{4}{\text{1⋅2}}+\frac{4}{\text{3⋅5}}+......+\frac{4}{\text{20⋅11⋅2013}}\)
Bài 5: So sánh với 1:
A=\(\frac{1}{\text{1⋅2}}+\frac{1}{\text{2⋅3}}+\frac{1}{\text{3⋅4}}+......+\frac{1}{\text{49⋅50}}\)
Bài 5 :
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{59}\)
\(A=1-\frac{1}{50}\)
từ trên ta có : \(1-\frac{1}{50}< 1\)
\(\Rightarrow A< 1\)
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Chưng minh rằng :
\(\frac{1.2-1}{2\text{!}}+\frac{2.3-1}{3\text{!}}+\frac{3.\text{4}-1}{\text{4}\text{!}}+...+\frac{99.100-1}{100\text{!}}< 2\)
\(\frac{1.2-1}{2!}+\frac{2.3-1}{3!}+\frac{3.4-1}{4!}+...+\frac{99.100-1}{100!}\)
\(=\frac{1.2}{2!}-\frac{1}{2!}+\frac{2.3}{3!}-\frac{1}{3!}+\frac{3.4}{4!}-\frac{1}{4!}+...+\frac{99.100}{100!}-\frac{1}{100!}\)
\(=1-\frac{1}{2!}+1-\frac{1}{3!}+\frac{1}{2!}-\frac{1}{4!}+...+\frac{1}{98!}-\frac{1}{100!}\)
\(=2-\frac{1}{99!}-\frac{1}{100!}< 2\)
Vậy \(\frac{1.2-1}{2!}+\frac{2.3-1}{3!}+\frac{3.4-1}{4!}+...+\frac{99.100-1}{100!}< 2\left(đpcm\right)\)