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\(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}.1\frac{1}{24}...1\frac{1}{99}\)
\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}....\frac{100}{99}\)
\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.\frac{5.5}{4.6}...\frac{10.10}{9.11}\)
\(=\frac{2.2.3.3.4.4.5.5....10.10}{1.3.2.4.3.5.4.6....9.11}\)
\(=\frac{\left(2.3.4.5....10\right)\left(2.3.4.5...10\right)}{\left(1.2.3.4.5...9\right)\left(3.4.5.6...11\right)}\)
\(=\frac{10.2}{11}\)
\(=\frac{20}{11}\)
Có gì không hiểu cứ hỏi nhé. Học tốt <3
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\(B=\left(1+\dfrac{1}{100}\right)\times\left(1+\dfrac{1}{99}\right)\times....\times\left(1+\dfrac{1}{3}\right)\times\left(1+\dfrac{1}{2}\right)\)
\(B=\dfrac{101}{100}\times\dfrac{100}{99}\times...\times\dfrac{4}{3}\times\dfrac{3}{2}\)
\(B=\dfrac{101\times100\times....\times4\times3}{100\times99\times....\times3\times2}\)
\(B=\dfrac{101}{2}\)
\(\Rightarrow B=\left(\dfrac{100}{100}+\dfrac{1}{100}\right)\times\left(\dfrac{99}{99}+\dfrac{1}{99}\right)\times...\times\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\times\left(\dfrac{2}{2}+\dfrac{1}{2}\right)\)
\(B=\dfrac{101}{100}\times\dfrac{100}{99}\times...\times\dfrac{4}{3}\times\dfrac{3}{2}\)
\(B=\dfrac{101}{2}\)( triệt tiêu các mẫu, tử giống nhau)
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3 câu như nhau cả thôi :v
\(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{55\cdot57}\)
\(A=\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{55\cdot57}\right)\)
\(A=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{55}-\frac{1}{57}\right)\)
\(A=\frac{1}{2}\left(1-\frac{1}{57}\right)\)
\(A=\frac{1}{2}\cdot\frac{56}{57}\)
\(A=\frac{28}{57}\)
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\(\Rightarrow x+\dfrac{1}{6}=\dfrac{3}{4}\\ \Rightarrow x=\dfrac{7}{12}\)
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a/\(x-\dfrac{5}{7}-\dfrac{13}{14}=1\)
\(x=1+\dfrac{5}{7}+\dfrac{13}{14}\)
\(x=\dfrac{14}{14}+\dfrac{10}{14}+\dfrac{13}{14}\)
\(x=\dfrac{37}{14}\)
Vậy \(x=\dfrac{37}{14}\)
b/\(\dfrac{3}{5}+x+1\dfrac{1}{5}=\dfrac{11}{3}\)
\(x+\dfrac{3}{5}+\dfrac{6}{5}=\dfrac{11}{3}\)
\(x+\dfrac{9}{5}=\dfrac{11}{3}\)
\(x=\dfrac{11}{3}-\dfrac{9}{5}\)
\(x=\dfrac{55}{15}-\dfrac{27}{15}\)
\(x=\dfrac{28}{15}\)
Vậy \(x=\dfrac{28}{15}\)
#kễnh
a) \(x-\dfrac{5}{7}-\dfrac{13}{14}=1\)
\(x-\dfrac{23}{14}=1\)
\(x=1+\dfrac{23}{14}\)
\(x=\dfrac{37}{14}\)
b) \(\dfrac{3}{5}+x+1\dfrac{1}{5}=\dfrac{11}{3}\)
\(x+1+\dfrac{3}{5}+\dfrac{1}{5}=\dfrac{11}{3}\)
\(x+\dfrac{9}{5}=\dfrac{11}{3}\)
\(x=\dfrac{11}{3}-\dfrac{9}{5}\)
\(x=\dfrac{28}{15}\)
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870 - x : 11 x 87 = 261
x : 11 x 87 = 870 - 261
x : 11 x 87 = 609
x : 11 = 609 : 87
x : 11 = 7
x = 7 x 11
x = 77
x : 0.25 x 2.3 = 6.9
x : 0.25 = 6.9 : 2.3
x : 0.25 = 3
x = 3 x 0.25
x = 0.75
2 x (y + y) = 8.16
y + y = 8.16 : 2
y x 2 = 4.08
y = 4.08 : 2
y = 2.04
y x 1.5 + y + y x 7.5 = 59.8
y x (1.5 + 1 + 7.5) = 59.8
y x 10 = 59.8
y = 59.8 : 10
y = 5.98
m : 1/6 + m : 0.25 = 152
m : 1/6 + m : 1/4 = 152
m x 6 + m x 4 = 152
m x (6 + 4) = 152
m x 10 = 152
m = 152 : 10
m = 15.2
m : 1/3 + m : 0.25 = 1.4
m : 1/3 + m : 1/4 = 1.4
m x 3 + m x 4 = 1.4
m x (3 + 4) = 1.4
m x 7 = 1.4
m = 1.4 : 7
m = 0.2
我不知道你是否理解
lây X ;2 là ra nha bạn