\(\left(1-\dfrac{1}{7}\right)\left(1-\dfrac{2}{7}\right)\left(1-\dfrac{3}{7}\right)...\left(1-\dfrac{2014}{7}\right)\)
Những câu hỏi liên quan
1. 25dfrac{1}{7}:left(-dfrac{5}{7}right)-15dfrac{1}{7}:left(-dfrac{5}{7}right)+dfrac{4}{5} 3. 2dfrac{2}{3}:left{left[left(3,72-0.02right)dfrac{10}{37}right]:dfrac{5}{6}+2,8right}-dfrac{7}{15}2. left(3+dfrac{4}{5}-dfrac{5}{12}right)left(dfrac{6}{7}-dfrac{3}{5}right)^24.23+3.left(-dfrac{1}{2}right)^2-22.4+left[left(-2right)^2:dfrac{1}{2}right]
Đọc tiếp
1. \(25\dfrac{1}{7}:\left(-\dfrac{5}{7}\right)-15\dfrac{1}{7}:\left(-\dfrac{5}{7}\right)+\dfrac{4}{5}\) 3. \(2\dfrac{2}{3}:\left\{\left[\left(3,72-0.02\right)\dfrac{10}{37}\right]:\dfrac{5}{6}+2,8\right\}-\dfrac{7}{15}\)
2. \(\left(3+\dfrac{4}{5}-\dfrac{5}{12}\right)\left(\dfrac{6}{7}-\dfrac{3}{5}\right)^2\)
4.23+3.\(\left(-\dfrac{1}{2}\right)^2\)-22.4+\(\left[\left(-2\right)^2:\dfrac{1}{2}\right]\)
2: \(=\dfrac{203}{60}\cdot\dfrac{81}{1225}=\dfrac{783}{3500}\)
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tính
\(G=\left(1-\dfrac{1}{7}\right)\left(1-\dfrac{2}{7}\right)\left(1-\dfrac{3}{7}\right)...\left(1-1\dfrac{2}{7}\right)\left(1-1\dfrac{3}{7}\right)\)
\(G=\left(1-\dfrac{1}{7}\right)\left(1-\dfrac{2}{7}\right)\left(1-\dfrac{3}{7}\right)\cdot...\cdot\left(1-1\dfrac{2}{7}\right)\left(1-1\dfrac{3}{7}\right)\\ =\left(1-\dfrac{1}{7}\right)\left(1-\dfrac{2}{7}\right)\left(1-\dfrac{3}{7}\right)\cdot...\left(1-\dfrac{7}{7}\right)...\left(1-1\dfrac{2}{7}\right)\left(1-1\dfrac{3}{7}\right)\\ =\left(1-\dfrac{1}{7}\right)\left(1-\dfrac{2}{7}\right)\left(1-\dfrac{3}{7}\right)\cdot...\cdot0\cdot...\cdot\left(1-1\dfrac{2}{7}\right)\left(1-1\dfrac{3}{7}\right)\\ =0\\ VậyG=0\)
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\(G=\left(1-\dfrac{1}{7}\right)\left(1-\dfrac{2}{7}\right)\left(1-\dfrac{3}{7}\right)...\left(1-1\dfrac{2}{7}\right)\left(1-1\dfrac{3}{7}\right)\)
\(\Leftrightarrow G=\left(1-\dfrac{1}{7}\right)\left(1-\dfrac{2}{7}\right)\left(1-\dfrac{3}{7}\right)....\left(1-\dfrac{7}{7}\right)...\left(1-1\dfrac{2}{7}\right)\left(1-1\dfrac{3}{7}\right)\)
\(\Leftrightarrow G=\left(1-\dfrac{1}{7}\right)\left(1-\dfrac{2}{7}\right)\left(1-\dfrac{3}{7}\right)...0....\left(1-1\dfrac{2}{7}\right)\left(1-1\dfrac{3}{7}\right)\)
\(\Leftrightarrow G=0\)
Vậy \(G=0\)
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Tính \(S=\left(\dfrac{-1}{7}\right)^0+\left(\dfrac{-1}{7}\right)^1+\left(\dfrac{-1}{7}\right)^2+\left(\dfrac{-1}{7}\right)^3+...+\left(\dfrac{-1}{7}\right)^{2017}\)
\(S=\left(-\dfrac{1}{7}\right)^0+\left(-\dfrac{1}{7}\right)^1+\left(-\dfrac{1}{7}\right)^2+....+\left(-\dfrac{1}{7}\right)^{2017}\\ =1+-\dfrac{1}{7}+\dfrac{1}{7^2}+-\dfrac{1}{7^3}+.....+-\dfrac{1}{7^{2017}}\\ =\left(1+\dfrac{1}{7^2}+\dfrac{1}{7^4}+...+\dfrac{1}{7^{2016}}\right)-\left(\dfrac{1}{7}+\dfrac{1}{7^3}+...+\dfrac{1}{7^{2017}}\right)\)
rồi bạn tính 2 về rồi trừ ra là xng nhé
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BT2: Tính nhanh
7) \(\left(-\dfrac{1}{2}\right)-\left(-\dfrac{3}{5}\right)+\left(-\dfrac{1}{9}\right)+\dfrac{1}{71}-\left(-\dfrac{2}{7}\right)+\dfrac{4}{35}-\dfrac{7}{18}\)
8)\(\left(3-\dfrac{1}{4}+\dfrac{2}{3}\right)-\left(5-\dfrac{1}{3}-\dfrac{6}{5}\right)-\left(6-\dfrac{7}{4}+\dfrac{3}{2}\right)\)
a, \(\dfrac{1}{24}-\left\{\dfrac{1}{4}-\left(\dfrac{1}{2}-\dfrac{7}{ }8\right)\right\}\)
b,\(\left(\dfrac{5}{7}-\dfrac{7}{5}\right)-\left\{\dfrac{1}{2}\left(\dfrac{2}{7}-\dfrac{1}{10}\right)\right\}\)
c,\(3-\left(\dfrac{-6}{7}\right)^6+\left(\dfrac{1}{2}\right)^2:2\)
d,\(\left(5^{-5}\right)^{-1}.\left(\dfrac{1}{2}\right)^2.\dfrac{1}{10^5}\)
Các bạn trả lời giúp mk nha. Mk đang cần gấp. Chều nay mk kiểm tra rồi
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2.Tính:
Aleft(dfrac{1}{10}-1right).left(dfrac{1}{11}-1right)left(dfrac{1}{12}-1right).....left(dfrac{1}{100}-1right)
Bleft(1-dfrac{1}{2^2}right)left(1-dfrac{1}{3^2}right)left(1-dfrac{1}{10^2}right)
Cleft(dfrac{7}{9}+1right)left(dfrac{7}{20}+1right)left(dfrac{7}{33}+1right)...left(dfrac{7}{108080}+1right)
Dleft(1-dfrac{28}{10}right)left(1-dfrac{52}{22}right)left(1-dfrac{80}{36}right)...left(1-dfrac{21808}{10900}right)
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2.Tính:
A=\(\left(\dfrac{1}{10}-1\right).\left(\dfrac{1}{11}-1\right)\left(\dfrac{1}{12}-1\right).....\left(\dfrac{1}{100}-1\right)\)
B=\(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)\left(1-\dfrac{1}{10^2}\right)\)
C=\(\left(\dfrac{7}{9}+1\right)\left(\dfrac{7}{20}+1\right)\left(\dfrac{7}{33}+1\right)...\left(\dfrac{7}{108080}+1\right)\)
D=\(\left(1-\dfrac{28}{10}\right)\left(1-\dfrac{52}{22}\right)\left(1-\dfrac{80}{36}\right)...\left(1-\dfrac{21808}{10900}\right)\)
\(\left(\dfrac{2}{3}-\dfrac{1}{2}-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}-\dfrac{1}{7}\right)\)
\(\left(\dfrac{15}{21}:\dfrac{5}{7}\right):\left(\dfrac{6}{5}:2\right)\)
a) \(\left(\dfrac{2}{3}-\dfrac{1}{2}-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{4}-\dfrac{1}{7}\right)\)
\(=-\dfrac{1}{6}\cdot\dfrac{17}{28}\)
\(=-\dfrac{17}{168}\)
b) \(\left(\dfrac{15}{21}\div\dfrac{5}{7}\right)\div\left(\dfrac{6}{5}\div2\right)\)
\(=1\div\dfrac{3}{5}\)
\(=\dfrac{5}{3}\)
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(2/3 - 1/2 - 1/3) . (1-1/4 - 1/7)
= -1/6 . 17/28
= -17/168
(15/21 : 5/7 ) : (6/5 : 2)
= 1 : 3/5
= 5/3
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Tính giá trị biểu thức :
\(\dfrac{1}{2}-\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\left(\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}\right)-\left(\dfrac{1}{5}+\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{4}{5}\right)+\left(\dfrac{1}{6}+\dfrac{2}{6}+\dfrac{3}{6}+\dfrac{4}{6}+\dfrac{5}{6}\right)-\left(\dfrac{1}{7}+\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{4}{7}+\dfrac{5}{7}+\dfrac{6}{7}\right)+...+\left(100+...+\dfrac{99}{100}\right)\)
12 tháng 12 2021 lúc 9:45
Tính :
B = \(\left(-\dfrac{1}{7}\right)^0+\left(-\dfrac{1}{7}\right)^1+\left(-\dfrac{1}{7}\right)^2+....+\left(-\dfrac{1}{7}\right)^{2018}\)
\(B=\left(-\dfrac{1}{7}\right)^0+\left(-\dfrac{1}{7}\right)^1+\left(-\dfrac{1}{7}\right)^2+...+\left(-\dfrac{1}{7}\right)^{2018}\)
\(\Rightarrow-\dfrac{1}{7}B=\left(-\dfrac{1}{7}\right)^1+\left(-\dfrac{1}{7}\right)^2+\left(-\dfrac{1}{7}\right)^3+...+\left(-\dfrac{1}{7}\right)^{2019}\)
\(\Rightarrow-\dfrac{1}{7}B-1=\left(-\dfrac{1}{7}\right)^1+\left(-\dfrac{1}{7}\right)^2+\left(-\dfrac{1}{7}\right)^3+...+\left(-\dfrac{1}{7}\right)^{2019}-\left(-\dfrac{1}{7}\right)^0-\left(-\dfrac{1}{7}\right)^1-\left(-\dfrac{1}{7}\right)^2-...-\left(-\dfrac{1}{7}\right)^{2018}\)
\(\Rightarrow-\dfrac{8}{7}B=\left(-\dfrac{1}{7}\right)^{2019}-1\)
\(\Rightarrow B=\left[\left(-\dfrac{1}{7}\right)^{2019}-1\right]:\left(-\dfrac{8}{7}\right)\)
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\(B=1-\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}+...-\dfrac{1}{7^{2017}}+\dfrac{1}{7^{2018}}\\ \Rightarrow7B=7-1+\dfrac{1}{7}-\dfrac{1}{7^2}+...-\dfrac{1}{7^{2016}}+\dfrac{1}{7^{2017}}\\ \Rightarrow7B+B=6+\dfrac{1}{7}-\dfrac{1}{7^2}+...+\dfrac{1}{7^{2017}}+1-\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}+...-\dfrac{1}{7^{2017}}+\dfrac{1}{7^{2018}}\\ \Rightarrow8B=7+\dfrac{1}{7^{2018}}=\dfrac{7^{2019}+1}{7^{2018}}\\ \Rightarrow B=\dfrac{7^{2019}+1}{8\cdot7^{2018}}\)
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