Tính nhanh:
D=\(\left(1-\frac{28}{10}\right)\left(1-\frac{52}{22}\right)\left(1-\frac{80}{36}\right).....\left(1-\frac{21808}{10900}\right)\)
K
Khách
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Những câu hỏi liên quan
NV
Nguyễn Việt Lâm
Giáo viên
24 tháng 2 2019
\(\left(1-\dfrac{28}{10}\right)\left(1-\dfrac{52}{22}\right)\left(1-\dfrac{80}{36}\right)...\left(1-\dfrac{21808}{10900}\right)\)
\(=\left(1-\dfrac{2.10+8}{10}\right)\left(1-\dfrac{2.22+8}{22}\right)\left(1-\dfrac{2.36+8}{36}\right)...\left(1-\dfrac{2.10900+8}{10900}\right)\)
\(=\left(1-2-\dfrac{8}{10}\right)\left(1-2-\dfrac{8}{22}\right)\left(1-2-\dfrac{8}{36}\right)...\left(1-2-\dfrac{8}{10900}\right)\)
\(=\left(-1-\dfrac{8}{1.10}\right)\left(-1-\dfrac{8}{2.11}\right)\left(-1-\dfrac{8}{3.12}\right)...\left(-1-\dfrac{8}{100.109}\right)\)
\(=\left(\dfrac{-18}{1.10}\right)\left(\dfrac{-30}{2.11}\right)\left(\dfrac{-44}{3.12}\right)...\left(\dfrac{-10908}{100.109}\right)\)
\(=\left(\dfrac{-2.9}{1.10}\right)\left(\dfrac{-3.10}{2.11}\right)\left(\dfrac{-4.11}{3.12}\right)...\left(\dfrac{-101.108}{100.109}\right)\)
\(=\dfrac{\left(-2\right)\left(-3\right)\left(-4\right)...\left(-101\right)}{1.2.3...100}.\dfrac{9.10.11...108}{10.11.12...109}\) (1)
\(=\dfrac{101}{1}.\dfrac{9}{109}=\dfrac{909}{109}\)
Do ở (1) có \(-2-\left(-101\right)+1=100\) nhân tử (số nhân tử là số chẵn) mang dấu âm nên kết quả sẽ mang dấu dương
S
20 tháng 1 2018
\(=\frac{-2}{3}\cdot\frac{-5}{6}\cdot\frac{-9}{10}\cdot\cdot\cdot\cdot\frac{-35}{36}\)
\(=\frac{-4}{6}\cdot\frac{-10}{12}\cdot\frac{-18}{20}\cdot\cdot\cdot\cdot\frac{-70}{72}\)
\(=\frac{-1.4}{2.3}\cdot\frac{-2.5}{3.4}\cdot\frac{-3.6}{4.5}\cdot\cdot\cdot\cdot\frac{-7.10}{8.9}\)
\(=\frac{\left(-1\right).\left(-2\right).\left(-3\right)...\left(-7\right)}{2.3.4....8}\cdot\frac{4.5.6....10}{3.4.5....9}\)
\(=\frac{\left(-1\right).2.3...7}{2.3.4....8}\cdot\frac{10}{3}\)
\(=\frac{-1}{8}\cdot\frac{10}{3}=\frac{-5}{12}\)
DN
21 tháng 1 2018
G=(1+8/10)(1+8/22)(1+8/36)...(1+8/8352)
18.30.44...8360
G=----------------------------
10.22.36...8352
9.2.10.3.11.4...95.88
G=-----------------------------------
10.1.11.2.12.3...96.87
(9.10.11...95)(2.3.4....88)
G= -----------------------------------------
(10.11.12...96)(2.3.4...87)
9.88.
G= ---------= 33/4.
96
botay.com.vn
D=18/10.30/22...........10908/10900
D=18.30........10908 / 10.22.10900
D=(2.9)(3.10).....(101.108) / (1.10)(2.11).....(100.109)
D=(2.3.......101)(9.10......108) / (1.2....100) (10.11....109)
D=101.9/109=909/109