A=7/10+7/10^2+7/10^3+......+7/10^100
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tìm A biết A =7/10 + 7/10^2+7/10^3+...+7/10^100
Chuyển thành Số thập phân A 2 1/10. 3 3/100. 6 7/10. 8 3/10. 17 9/10. 12 7 10. Làm nhanh giúp mình với
2\(\dfrac{1}{10}\) = 2 + \(\dfrac{1}{10}\) = 2 + 0,1 = 2,1
3\(\dfrac{3}{100}\) = 3 + \(\dfrac{3}{100}\) = 3 + 0,03 = 3,03
6\(\dfrac{7}{10}\) = 6 + \(\dfrac{7}{10}\) = 6 + 0,7 = 6,7
8\(\dfrac{3}{10}\) = 8 + \(\dfrac{3}{10}\) = 8 + 0,3 = 8,3
17\(\dfrac{9}{10}\) = 17 + \(\dfrac{9}{10}\) = 17 + 0,9 = 17,9
12\(\dfrac{7}{10}\) = 12 + \(\dfrac{7}{10}\) = 12 + 0,7 = 12,7
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7/10+7/10^2+...+7/10^99+7/10^100
\(10A=7+\frac{7}{10}+\frac{7}{10^2}+...+\frac{7}{10^{99}}\)
\(10A-A=\left(7+\frac{7}{10}+...+\frac{7}{10^{99}}\right)-\left(\frac{7}{10}+\frac{7}{10^2}+...+\frac{7}{10^{100}}\right)\)
\(9A=7-\frac{7}{10^{100}}\)
\(A=\frac{7-\frac{7}{10^{100}}}{9}\)
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Các bn ghi rõ cách làm nha mk đang cần gấp nhank mk tick cho
A= 3/7*10+3/10*13+...+3/100*103
B= 2/7*10+2/10*13+...+2/100*103
\(\frac{3}{7.10}+\frac{3}{10.13}+....+\frac{3}{100.103}\)
\(=\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+....+\frac{1}{100}-\frac{1}{103}\)
\(=\frac{1}{7}-\frac{1}{103}\)
\(=\frac{96}{721}\)
\(\frac{2}{7.10}+\frac{2}{10.13}+...+\frac{2}{100.103}\)
\(=\frac{2}{3}\left(\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{100}-\frac{1}{103}\right)\)
\(=\frac{2}{3}\left(\frac{1}{7}-\frac{1}{103}\right)\)
\(=\frac{2}{3}.\frac{96}{721}\)
\(=\frac{64}{721}\)
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Các bn ghi rõ cách giải nha mk đang rất cần gấp nhank mk tick cho
A= 3/7*10+3/10*13+...+3/100*103
B= 2/7*10+2/10*13+...+2/100*103
\(A=\)\(\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{100.103}\)
\(A=\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{100}-\frac{1}{103}\)
\(A=\frac{1}{7}-\frac{1}{103}\)
\(A=\frac{96}{721}\)
\(B=\frac{2}{7.10}+\frac{2}{10.13}+...+\frac{2}{100.103}\)
\(B=2\left(\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{100.103}\right)\)
\(3B=2.3\left(\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{100.103}\right)\)
\(3B=2\left(\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{100.103}\right)\)
\(3B=2\left(\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{100}-\frac{1}{103}\right)\)
\(3B=2\left(\frac{1}{7}-\frac{1}{103}\right)\)
\(3B=2.\frac{96}{721}\)
\(3B=\frac{192}{721}\)
\(\Rightarrow B=\frac{192}{721}:3\)
\(B=\frac{64}{721}\)
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\(A=\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{100.103}\)
\(A=\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{100}-\frac{1}{103}\)
\(A=\frac{1}{7}-\frac{1}{103}\)
\(A=\frac{96}{721}\)
Vậy \(A=\frac{96}{721}\)
\(B=\frac{2}{7.10}+\frac{2}{10.13}+...+\frac{2}{100.103}\)
\(B=\frac{2}{3}.\left(\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{100.103}\right)\)
\(B=\frac{2}{3}.\left(\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{100}-\frac{1}{103}\right)\)
\(B=\frac{2}{3}.\left(\frac{1}{7}-\frac{1}{103}\right)\)
\(B=\frac{2}{3}.\frac{96}{721}\)
\(B=\frac{64}{721}\)
Vậy \(B=\frac{64}{721}\)
_Chúc bạn học tốt_
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A, X = 2 x 10 000 + 2 x 1000 +5 x 100+9 x 10+7
B, X =7 x 100 000 + 7 x 10 000 + 8 x 100 + 5
C, X= 4 x 10 000 +6 x 100 + 3 x 10
D, X= 1 x 100 000 + A x 1000 + 2 x100 + 1 x 10 + B
MONG CAC BAN LAM GIUP MINH
Tính tổng
A=\(\frac{7}{10}+\frac{7}{10^2}+...+\frac{7}{10^{99}}+\frac{7}{10^{100}}\)
\(A=\frac{7}{10}+\frac{7}{10^2}+...+\frac{7}{10^{100}}\)
\(10A=7+\frac{7}{10}+...+\frac{7}{10^{99}}\)
\(\Rightarrow10A-A=9A=7-\frac{7}{10^{100}}\)
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Ta có : \(10A=7+\frac{7}{10}+\frac{7}{10^2}+...+\frac{7}{10^{99}}\)
\(A=\frac{7}{10}+\frac{7}{10^2}+...+\frac{7}{10^{99}}+\frac{7}{10^{100}}\)
\(\Rightarrow9A=10A-A=7-\frac{7}{10^{100}}\)
\(\Rightarrow A=\frac{7-\frac{7}{10^{100}}}{9}\)
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a=7/10+7/10^2+7/10^3+...+7/10^2011
\(A=\dfrac{7}{10}+\dfrac{7}{10^2}+\dfrac{7}{10^3}+...+\dfrac{7}{10^{2011}}\)
\(\Rightarrow10A=7+\dfrac{7}{10}+\dfrac{7}{10^2}+...+\dfrac{7}{10^{2010}}\)
\(\Rightarrow10A-A=7+\dfrac{7}{10}+\dfrac{7}{10^2}+...+\dfrac{7}{10^{2010}}-\left(\dfrac{7}{10}+\dfrac{7}{10^2}+\dfrac{7}{10^3}+...+\dfrac{7}{10^{2011}}\right)\)
\(\Rightarrow9A=7-\dfrac{7}{10^{2011}}\)
\(\Rightarrow A=\dfrac{7}{9}.\left(1-\dfrac{1}{10^{2011}}\right)\)
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A=7/10+7/10^2+7/10^3+..............+7/10^2018