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6 tháng 3 2016

\(\frac{5}{14}\)

6 tháng 3 2016

A=\(\frac{1}{2}\)+\(\frac{5}{6}\)+\(\frac{11}{12}\)+\(\frac{19}{20}\)+\(\frac{29}{30}\)+\(\frac{41}{42}\)=(1-\(\frac{1}{2}\))+(1-\(\frac{1}{6}\))+(1-\(\frac{1}{12}\))+(1-\(\frac{1}{20}\))+(1-\(\frac{1}{30}\))+(1-\(\frac{1}{42}\))

  =1-1+\(\frac{1}{2}\)+1-\(\frac{1}{2}\)+\(\frac{1}{3}\)+1-\(\frac{1}{3}\)+\(\frac{1}{4}\)+1-\(\frac{1}{4}\)+\(\frac{1}{5}\)+1-\(\frac{1}{5}\)+\(\frac{1}{6}\)+1-\(\frac{1}{6}\)+\(\frac{1}{7}\)

  =(1-1+1+1+1+1+1)+(\(\frac{1}{2}\)-\(\frac{1}{2}\))+(\(\frac{1}{3}\)-\(\frac{1}{3}\))+(\(\frac{1}{4}\)-\(\frac{1}{4}\))+(\(\frac{1}{5}\)-\(\frac{1}{5}\))+(\(\frac{1}{6}\)-\(\frac{1}{6}\))+\(\frac{1}{7}\)

  =5+\(\frac{1}{7}\)=\(\frac{36}{7}\)

15 tháng 10 2016

=\(\frac{619}{120}\)

k cho mk nha

=1/1.2+5/2.3+11/3.4+19/4.5+29/5.6+41/6.7

=1-1/2+5/2-5/3+11/3-11/4+19/4-19/5+29/5-29/6+41/6-41/7

=3+2+2+2+2-41/7

=77/7-41/7

=36/7

k nhé

\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}\)

\(=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+\left(1-\frac{1}{20}\right)+\left(1-\frac{1}{30}\right)+\left(1-\frac{1}{42}\right)\)

\(=\left(1+1+1+1+1+1\right)-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)

\(=6-\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}\right)\)

\(=6-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)

\(=6-\left(1-\frac{1}{7}\right)=6-\frac{6}{7}=\frac{36}{7}\)

22 tháng 4 2018

đề bài đâu mà tính

22 tháng 4 2018

đề đâu

31 tháng 8 2015

=> A = ( 1 - 1/2 ) + ( 1 - 1/6 ) + ( 1 - 1/12 ) + ( 1 - 1/30 ) + .... + ( 1 - 1/90 )

=> A = ( 1 + 1 + 1 + .... 1 ) - ( 1/2 + 1/6 + 1/12 + 1/30 + .... + 1/90 )

=> A = 9 - ( 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + .... + 1/9.10 )

=> A = 9 - ( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10 )

=> A = 9 - ( 1 - 1/10 )

=> A = 9 - 9/10

=> 81/10

17 tháng 2 2017

81/10

3 tháng 5 2016

A=1-1/2+1-1/6+...+1-1/90

  =9-(1/2+1/6+...+1/90) =9-(1/1.2+1/2.3+...+1/9.10)

  =9-(1-1/10)=9-9/10=81/10

23 tháng 2 2016

\(\frac{1}{2}+\frac{5}{6}+...+\frac{55}{56}\)

\(=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+...+\left(1-\frac{1}{56}\right)\)

\(=7.1-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{56}\right)\)

\(=7-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{7.8}\right)\)

\(=7-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{7}-\frac{1}{8}\right)\)

\(=7-\left(1-\frac{1}{8}\right)\)

\(=7-\frac{7}{8}=\frac{49}{8}\)

23 tháng 2 2016

\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}=\frac{1889}{312}\)

7 tháng 7 2018

\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}\) \(\frac{89}{90}\)

\(=(1-\frac{1}{2})+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+\left(1-\frac{1}{20}\right)+\left(1-\frac{1}{30}\right)+\left(1-\frac{1}{42}\right)+\left(1-\frac{1}{56}\right)\) \(+\left(1-\frac{1}{72}\right)+\left(1-\frac{1}{90}\right)\)

\(=\left(1+1+1+1+1+1+1+1+1\right)-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)

\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\) 

\(=9-\frac{11}{10}\)

\(=\frac{79}{10}\)

~Học tốt nha~

7 tháng 7 2018

Đặt : \(A=\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}\)

\(\Leftrightarrow A=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+......+\left(1-\frac{1}{90}\right)\)

\(\Leftrightarrow A=\left(1+1+....+1\right)-\left(\frac{1}{2}+\frac{1}{6}+....+\frac{1}{90}\right)\)

\(\Leftrightarrow A=9-\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)

\(\Leftrightarrow A=9-\left(1-\frac{1}{10}\right)\)

\(\Leftrightarrow A=9-\frac{9}{10}=\frac{81}{90}\)

23 tháng 6 2016

=1 nhe

=(1-1/2)+(1-1/6)+(1-1/12)+...+(1-1/90)

=9-(1/2 + 5/6 + 1/12 + ... + 1/90)

=9-(1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10)

=9-(1-1/10)

=9-9/10=81/10