`A=4/(1.2)+4/(2.3)+4/(3.4)+......+4/(2014.2015)`
`=4(1/(1.2)+1/(2.3)+1/(3.4)+......+1/(2014.2015))`
`=4(1-1/2+1/2-1/3+1/3-1/4+....+1/2014-1/2015)`
`=4(1-1/2015)`
`=4. 2014/2015`
`=8056/2015`

A=4.(1/1.2+1/2.3+...+1/2014.2015)

A=4.(1-1/2+1/2-1/3+...+1/2014-1/2015)

A=4.(1-1/2015)

A=4.2014/2015

A=8056/2015

Giải:

\(A=\dfrac{4}{1.2}+\dfrac{4}{2.3}+\dfrac{4}{3.4}+...+\dfrac{4}{2014.2015}\) 

\(A=4.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2014.2015}\right)\) 

\(A=4.\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2014}-\dfrac{1}{2015}\right)\) 

\(A=4.\left(\dfrac{1}{1}-\dfrac{1}{2015}\right)\) 

\(A=4.\dfrac{2014}{2015}\) 

\(A=\dfrac{8056}{2015}\)

\(A=\frac{4}{1.2}+\frac{4}{2.3}+...+\frac{4}{2014.2015}\)

\(A=4\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2014.2015}\right)\)

\(A=4\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2014}-\frac{1}{2015}\right)\)

\(A=4\left(\frac{1}{1}-\frac{1}{2015}\right)\)

\(A=4\left(\frac{2015-1}{2015}\right)\)

\(A=4.\frac{2014}{2015}\)

... BẠN TỰ LÀM NỐT NHÉ!

\(\frac{4}{1\cdot2}+\frac{4}{2\cdot3}+...+\frac{4}{2014\cdot2015}\)

\(=4\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+....+\frac{1}{2014\cdot2015}\right)\)

\(=4\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2014}-\frac{1}{2015}\right)\)

\(=4\left(1-\frac{1}{2015}\right)\)

\(=4\cdot\frac{2014}{2015}=\frac{8056}{2015}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2014}-\frac{1}{2015}\)

\(=1-\frac{1}{2015}\)

\(=\frac{2014}{2015}\)

A=1/1-1/2+1/2-1/3+1/3-...........+1/2014-1/2015

A=1/1-1/2015

A=2014/2015

=1-1/2+1/2-1/3+1/3-1/4+....+1/2014-1/2015

Trừ tất cả ta được 1-1/2015=2014/2015

=1-1/2+1/2-1/3+1/3-1/4+.....+1/2014-1/2015

=1-1/2015=2014/2015

=1-(1/2+1/2-1/3+1/3-1/4+...+1/2014-1/2015)

=1-1/2015                           

=2014/2015.   

Nếu đúng thì nhớ tíck cho mk nhé!!!Thanh you...

\(A=4\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2014}-\dfrac{1}{2015}\right)\)

\(=4\cdot\dfrac{2014}{2015}=\dfrac{8056}{2015}\)

1.

a. \(\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+...+\frac{5}{99.100}\)

\(=5.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)

\(=5.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(=5.\left(1-\frac{1}{100}\right)\)

\(=5.\frac{99}{100}\)

\(=\frac{99}{20}\)

b. \(\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{99.101}\)

\(=2.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{99.101}\right)\)

\(=2.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\frac{4}{2}.\left(1-\frac{1}{101}\right)\)

\(=2.\frac{100}{101}\)

\(=\frac{200}{101}\)

Đặt \(A=\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{99.101}\)

\(\Rightarrow\frac{1}{2}A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)

\(\Rightarrow\frac{1}{2}A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

\(\Rightarrow\frac{1}{2}A=1-\frac{1}{101}\)

\(\Rightarrow\frac{1}{2}A=\frac{100}{101}\)

\(\Rightarrow A=\frac{100}{101}.2\)

\(\Rightarrow A=\frac{200}{101}.\)