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16 tháng 6 2017
\(a.\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\)
\(=\frac{1}{2}-\frac{1}{5}\)
\(=\frac{3}{10}\)
\(b.\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}\)
\(=2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}\right)\)
\(=2\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\right)\)
\(=2\cdot\left(\frac{1}{2}-\frac{1}{5}\right)\)
\(=2\cdot\frac{3}{10}=\frac{3}{5}\)
\(c.\frac{1}{2\cdot3}+\frac{2}{3\cdot5}+\frac{3}{5\cdot8}\)
\(=\frac{1}{6}+\frac{2}{15}+\frac{3}{40}\)
\(=\frac{3}{8}\)
k nha 500 AE
DP
16 tháng 6 2017
a, \(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}\)
\(=\frac{3-2}{2\times3}+\frac{4-3}{3\times4}+\frac{5-4}{4\times5}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\)
\(=\frac{1}{2}-\frac{1}{5}\)
\(=\frac{3}{10}\)
b, \(\frac{2}{2\times3}+\frac{2}{3\times4}+\frac{2}{4\times5}\)
\(=\frac{3-2}{2\times3}+\frac{4-3}{3\times4}+\frac{5-4}{4\times5}\)
\(=\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\right)\times\frac{2}{1}\)
\(=\left(\frac{1}{2}-\frac{1}{5}\right)\times\frac{2}{1}\)
\(=\frac{3}{10}\times\frac{2}{1}\)
\(=\frac{3}{5}\)
c, \(\frac{1}{2\times3}+\frac{2}{3\times5}+\frac{3}{5\times8}\)
\(=\frac{3-2}{2\times3}+\frac{5-3}{3\times5}+\frac{8-5}{5\times8}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}\)
\(=\frac{1}{2}-\frac{1}{8}\)
\(=\frac{3}{8}\)
28 tháng 8 2017
1 \(A=\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)\times\left(1+\frac{1}{4}\right)\times.........\times\left(1+\frac{1}{2016}\right)\times\left(1+\frac{1}{2017}\right)\)
\(A=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times......\times\frac{2016}{2017}\times\frac{2018}{2017}\)
\(A=\frac{2018}{2}=1009\)
\(B=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+.......+\frac{2}{43.45}\)
\(B=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-......+\frac{1}{43}-\frac{1}{45}\)
\(B=\frac{1}{3}-\frac{1}{45}\)
\(B=\frac{14}{45}\)
2 \(\frac{2017}{2018}\times\frac{23}{47}+\frac{24}{2018}\times\frac{2017}{47}\)
\(=\frac{2017}{2018}\times\frac{23}{47}+\frac{24}{47}\times\frac{2017}{2018}\)
\(=\frac{2017}{2018}\times\left(\frac{23}{47}+\frac{24}{47}\right)\)
\(=\frac{2017}{2018}\times1\)
=\(\frac{2017}{2018}\)
bạn nào xem giải thế có đúng ko
CT
11
26 tháng 4 2017
\(\frac{1}{2}+\frac{1}{2}=\frac{1+1}{2}=\frac{2}{2}=1\)
\(\frac{3}{4}+\frac{1}{4}=\frac{3+1}{4}=\frac{4}{4}=1\)
\(\frac{3}{9}+\frac{6}{9}=\frac{3+6}{9}=\frac{9}{9}=1\)
M
15 tháng 8 2017
ta có : A=1/2+1/4+..+1/1024
=> A=1/21+1/22+..+1/210
=> A.2=(1/21+1/22+..+1/210).2
=> A.2=1+1/21+1/22+..+1/29
=> 2A-A=(1+1/21+1/22+..+1/29)-(1/21+1/22+..+1/210)
=> A=1-1/210
7 tháng 7 2018
a) \(\frac{3}{5}\times y+\frac{1}{2}:\frac{5}{3}-\frac{5}{4}=\frac{1}{2}\times\frac{1}{3}\)
\(\Rightarrow\frac{3}{5}\times y+\frac{3}{10}-\frac{5}{4}=\frac{1}{6}\)
\(\Rightarrow\frac{3}{5}\times y+\left(-\frac{19}{20}\right)=\frac{1}{6}\)
\(\Rightarrow\frac{3}{5}\times y=\frac{67}{60}\)
\(\Rightarrow y=\frac{67}{36}\)
b) \(\frac{4}{5}:y+\frac{1}{4}\times\frac{1}{6}-\frac{1}{2}=\frac{1}{3}\times\frac{5}{2}\)
\(\Rightarrow\frac{4}{5}:y+\frac{1}{24}-\frac{1}{2}=\frac{5}{6}\)
\(\Rightarrow\frac{4}{5}:y+\left(-\frac{11}{24}\right)=\frac{5}{6}\)
\(\Rightarrow\frac{4}{5}:y=\frac{5}{6}+\frac{11}{24}=\frac{31}{24}\)
\(\Rightarrow y=\frac{4}{5}:\frac{31}{24}=\frac{96}{155}\)
c) \(\frac{3}{5}\times y-\frac{4}{5}:3+\frac{1}{12}=\frac{3}{2}+\frac{1}{5}\)
\(\Rightarrow\frac{3}{5}\times y-\frac{4}{15}+\frac{1}{12}=\frac{17}{10}\)
\(\Rightarrow\frac{3}{5}\times y-\frac{4}{15}=\frac{97}{60}\)
\(\Rightarrow\frac{3}{5}\times y=\frac{113}{60}\)
\(\Rightarrow y=\frac{113}{36}\)
DL
1 tháng 6 2017
\(\frac{1}{2}:\frac{3}{2}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\)
\(=\frac{1\cdot\left(2\cdot5\cdot6\cdot7\right)}{8\cdot3\cdot\left(2\cdot5\cdot6\cdot7\right)}\)
\(=\frac{1}{24}\)
DL
1 tháng 6 2017
\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}\)
\(=\frac{1\cdot\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)}{\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)\cdot10}\)
\(=\frac{1}{10}\)
NN
13 tháng 6 2020
\(\left(1-\frac{2}{5}\right)\times\left(1-\frac{2}{7}\right)\times\left(1-\frac{2}{9}\right)\times\left(1-\frac{2}{11}\right)\times\left(1-\frac{2}{13}\right)\)
\(=\frac{3}{5}\times\frac{5}{7}\times\frac{7}{9}\times\frac{9}{11}\times\frac{11}{13}=\frac{3}{13}\)
1 tháng 9 2016
b) 1/3+1/3^2+1/3^3+1/3^4+1/3^5 (goi tong bang M)
3M=1+1/3+1/3^2+1/3^3+1/3^4
3M-M=1-1/3^5
2M=242/243
M=242/243*1/2=121/243
Trả lời:
2/2750+ 2748/2750=1
2/2750+...................=1
=>.................=1-2/2750
=>....................=2748/2750