Tính:
\(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}.1\frac{1}{24}.....1\frac{1}{9800}\)
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2 tháng 2 2016
\(A=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}.\frac{36}{35}......\frac{9801}{9800}=\frac{\left(2.3.4.5....99\right)^2}{1.3.2.4.3.5.4.6.....98.100}=\frac{2.3.4.5...99}{1.2.3.4.....98}.\frac{2.3.4.5....99}{3.4.5.6......100}=\frac{99}{1}.\frac{2}{100}=\frac{99}{50}\)
P
3
T
18 tháng 7 2019
#)Giải :
\(1\frac{1}{3}\times1\frac{1}{8}\times1\frac{1}{15}\times...\times1\frac{1}{9800}\)
\(=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times...\times\frac{9801}{9800}\)
\(=\frac{2.2}{1.3}\times\frac{3.3}{2.4}\times\frac{4.4}{3.5}\times...\times\frac{99.99}{98.100}\)
\(=\frac{2.3.4.....99}{1.2.3.....98}\times\frac{2.3.4.....99}{3.4.5.....100}\)
\(=99\times\frac{2}{100}=\frac{198}{100}=\frac{99}{50}\)
A
18 tháng 7 2019
\(=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times...\times\frac{9801}{9800}\)
\(=\frac{2.2}{1.3}\times\frac{3.3}{2.4}\times\frac{4.4}{3.5}\times...\times\frac{99.99}{98.100}\)
\(=\frac{2.3.4.5.....99}{1.2.3.4....98}\times\frac{2.3.4.5.....99}{3.4.5.6.....100}\)
\(=\frac{99}{1}\times\frac{2}{100}\)
\(=\frac{99}{50}\)
HC
0
PN
0
6 tháng 3 2020
\(1\frac{1}{30}:\left(24\frac{1}{6}-24\frac{1}{5}\right)-\frac{1\frac{1}{2}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(-1\frac{1}{15}\right):\left(8\frac{1}{5}-8\frac{1}{3}\right)\)
\(\Rightarrow\frac{31}{30}:\left(\frac{145}{6}-\frac{121}{5}\right)-\frac{\frac{3}{2}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(\frac{-16}{15}\right):\left(\frac{41}{5}-\frac{25}{3}\right)\)
\(\Rightarrow\frac{31}{30}:\left(\frac{725}{30}-\frac{726}{30}\right)-\frac{\frac{6}{4}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(\frac{-16}{15}\right):\left(\frac{123}{15}-\frac{125}{15}\right)\)
\(\Rightarrow\frac{31}{30}:\frac{-1}{30}-\frac{\frac{3}{4}}{4x-\frac{1}{2}}=\frac{-16}{15}:\frac{-2}{15}\)
\(\Rightarrow\frac{31}{30}.\frac{30}{-1}-\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\frac{-16}{15}.\frac{15}{-2}\)
\(\Rightarrow\left(-31\right)-\frac{3}{4}:\left(4x-\frac{1}{2}\right)=8\)
\(\Rightarrow\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\left(-31\right)-8\)
\(\Rightarrow\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\left(-39\right)\)
\(\Rightarrow4x-\frac{1}{2}=\frac{3}{4}:\left(-39\right)\)
\(\Rightarrow4x-\frac{1}{2}=\frac{3}{4}.\frac{-1}{39}\)
\(\Rightarrow4x-\frac{1}{2}=\frac{-1}{52}\)
\(\Rightarrow4x=\frac{-1}{52}+\frac{1}{2}\)
\(\Rightarrow4x=\frac{-1}{52}+\frac{26}{52}\)
\(\Rightarrow4x=\frac{25}{52}\)
\(\Rightarrow x=\frac{25}{52}:4\)
\(\Rightarrow x=\frac{25}{52}.\frac{1}{4}\)
\(\Rightarrow x=\frac{25}{208}\)
Vậy \(x=\frac{25}{208}\)
Chúc bn học tốt
\(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}....1\frac{1}{9800}=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}....\frac{9801}{9800}\)
\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}....\frac{99.99}{98.100}\)
\(=\frac{2.3.4...99}{1.2.3....98}.\frac{2.3.4...99}{3.4.5...100}\)
\(=99.\frac{2}{100}=99.\frac{1}{50}=\frac{99}{50}\)
aweee tks <3