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29 tháng 8 2018

\(-\frac{1}{1.2}+-\frac{1}{2.3}+-\frac{1}{3.4}+-\frac{1}{4.5}\)

\(=-1\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}\right)\)

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

\(=-1\left(1-\frac{1}{5}\right)\)

\(=-1.\frac{4}{5}=-\frac{4}{5}\)

29 tháng 8 2018

\(\frac{-1}{1.2}+\frac{-1}{2.3}+\frac{-1}{3.4}+\frac{-1}{4.5}\)

\(=-1\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}\right)\)

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

\(=-1\left(1-\frac{1}{5}\right)\)

\(=-1.\frac{4}{5}=-\frac{4}{5}\)

18 tháng 9 2018

=>-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5)

=>-(1-1/5)

=>-4/5

18 tháng 9 2018

\(\:\frac{-1}{1.2}+\frac{-1}{2.3}+\frac{-1}{3.4}+\frac{-1}{4.5}\)

\(=-1\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}\right)\)

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

=\(-1\left(1-\frac{1}{5}\right)\)

=\(-1\times\frac{4}{5}\)

=\(\frac{-4}{5}\)

31 tháng 3 2019

Làm bậy, mà đúng

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{2.4}+...+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)

31 tháng 3 2019

\(\frac{1}{1.2}\)\(\frac{1}{2.3}\)\(\frac{1}{3.4}\)\(\frac{1}{4.5}\)+ … + \(\frac{1}{99.100}\)

\(\frac{1}{1}\)\(\frac{1}{2}\)\(\frac{1}{2}\)\(\frac{1}{3}\)\(\frac{1}{3}\)-\(\frac{1}{4}\)\(\frac{1}{4}\)\(\frac{1}{5}\)+ … + \(\frac{1}{99}\)\(\frac{1}{100}\)

\(\frac{1}{1}\)\(\frac{1}{100}\)

\(\frac{99}{100}\)

14 tháng 7 2018

\(x-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}=\frac{1}{4.5}\)

\(x-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}-\frac{1}{4.5}=0\)

\(x-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}\right)=0\)

\(x-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\right)=0\)

\(x-\left(1-\frac{1}{5}\right)=0\)

\(x-\frac{4}{5}=0\)

\(x=\frac{4}{5}\)

14 tháng 7 2018

\(x-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}=\frac{1}{4.5}\)

\(x-\left(1-\frac{1}{2}\right)-\left(\frac{1}{2}-\frac{1}{3}\right)-\left(\frac{1}{3}-\frac{1}{4}\right)=\frac{1}{4}-\frac{1}{5}\)

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

\(x-1=-\frac{1}{5}\)

\(x=\frac{4}{5}\)

1 tháng 10 2016

Ta có 

\(1+\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{9.10}\)

\(=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{9}-\frac{1}{10}\)

\(=2-\frac{1}{10}\)

\(=\frac{19}{10}\)

Vậy \(1+\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{9.10}\)\(=\frac{19}{10}\)

3 tháng 5 2018

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

                                                                     \(=1-\frac{1}{6}\)

                                                                     \(=\frac{5}{6}\)

3 tháng 5 2018

1/1.2+1/2.3+1/3.4+1/4.5+1/5.6

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6

=1-1/6

=5/6

10 tháng 5 2017

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2016\cdot2017}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}\)

\(=1-\frac{1}{2017}=\frac{2016}{2017}\)

30 tháng 3 2017

\(M=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)

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

\(M=1-\frac{1}{7}\)

\(M=\frac{6}{7}\)

30 tháng 3 2017

6/7

k cho mình nha

19 tháng 4 2017

\(=\frac{1}{1.2}-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{10}\)

\(=\frac{1}{10}\)

19 tháng 4 2017

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

1-1/10=9/10

nhớ cho mk

11 tháng 5 2020

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

\(A=1-\frac{1}{6}=\frac{5}{6}\)

\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{n}-\frac{1}{n+1}\)

\(B=1-\frac{1}{n+1}=\frac{n}{n+1}\)

15 tháng 7 2018

\(\frac{1}{9.10}-\frac{1}{8.9}-\frac{1}{7.8}-\frac{1}{6.7}-\frac{1}{5.6}-\frac{1}{4.5}-\frac{1}{3.4}-\frac{1}{2.3}-\frac{1}{1.2}\)

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

\(=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\right)+\frac{1}{90}\)

\(=-\left(1-\frac{1}{10}\right)+\frac{1}{90}\)

\(=-\frac{9}{10}+\frac{1}{90}\)

= ...

bn tự tính nha!