A= \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2018.2019}\)

A= 1 - \(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{2018}-\frac{1}{2019}\)

A= 1 - \(\frac{1}{2019}\)

A= \(\frac{2018}{2019}\)

\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{2018\cdot2019}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2018}-\frac{1}{2019}\)

\(A=1-\frac{1}{2019}\)

\(=\frac{2018}{2019}\)

Vậy \(A=\frac{2018}{2019}\)

HOK TỐT ==.==

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{2018.2019}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-.....-\frac{1}{2019}\)

\(\Rightarrow A=1-\frac{1}{2019}\)

\(\Rightarrow A=\frac{2019}{2019}-\frac{1}{2019}=\frac{2018}{2019}\)

Vậy A = \(\frac{2018}{2019}\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)

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

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

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

_Chúc bạn học tốt_

Ta có : \(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)

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

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

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)

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

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

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

hi bn

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

     \(\frac{1313}{1212}:x=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\)\(\frac{1}{5.6}\)

\(\Leftrightarrow\frac{13}{12}:x=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(\Leftrightarrow\frac{13}{12}:x=1-\frac{1}{6}\)

\(\Leftrightarrow\frac{13}{12}:x=\frac{5}{6}\)

\(\Leftrightarrow x=\frac{13}{12}:\frac{5}{6}\)

\(\Leftrightarrow x=\frac{13}{10}\)

  Vậy \(x=\frac{13}{10}\)

                            ~~~~~Hok tốt ~~~~~

a,\(\frac{1313}{1212}\div x=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)

\(\frac{13}{12}\div x=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(\frac{13}{12}\div x=1-\frac{1}{6}\)

\(\frac{13}{12}\div x=\frac{5}{6}\)

\(x=\frac{13}{12}\div\frac{5}{6}\)

\(x=\frac{13}{12}\times\frac{6}{5}\)

\(x=\frac{13}{10}\)

Chúc bạn hok tốt !

\(\frac{1313}{1212}:x=\frac{1}{1x2}+\frac{1}{2x3}+...+\frac{1}{5x6}\)

\(\frac{1313}{1212}:\frac{101}{101}=\frac{13}{12}:x=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{5}-\frac{1}{6}\)

\(\frac{13}{12}:x=1-\frac{1}{6}\)

\(\frac{13}{12}:x=\frac{5}{6}\)

\(x=\frac{13}{12}:\frac{5}{6}\)

\(x=\frac{78}{60}=\frac{13}{10}\)

       \(\frac{1313}{1212}:x=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\)\(\frac{1}{5.6}\)

\(\Leftrightarrow\frac{13}{12}:x=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(\Leftrightarrow\frac{13}{12}:x=1-\frac{1}{6}\)

\(\Leftrightarrow\frac{13}{12}:x=\frac{5}{6}\)

\(\Leftrightarrow x=\frac{13}{12}:\frac{5}{6}\)

\(\Leftrightarrow x=\frac{13}{10}\)

                  Hok tốt

\(A=\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{49.50}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{49}-\frac{1}{50}=\frac{1}{1}-\frac{1}{50}=\frac{49}{50}\)

Vậy A=49/50

Công thức: \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{19\cdot20}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{19}-\dfrac{1}{20}\)

\(=1-\dfrac{1}{20}=\dfrac{19}{20}\)

\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+....+\dfrac{1}{19\cdot20}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+....+\dfrac{1}{19}-\dfrac{1}{20}\)

\(A=1-\dfrac{1}{20}\)

\(A=\dfrac{19}{20}\)

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

=1-1/6

=5/6

Tick