\(A=4\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2014}-\dfrac{1}{2015}\right)=4\left(\dfrac{1}{1}-\dfrac{1}{2015}\right)=\dfrac{8056}{2015}\)
`A=4/(1.2) + 4/(2.3) + 4/(3.4) + ... + 4/(2014.2015)`
`=4. (1/(1.2) + 1/(2.3) + ... + 1/(2014.2015))`
`= 4 . [ (1/1 - 1/2) + (1/2 - 1/3) + ... + (1/2014 - 1/2015)]`
`= 4.(1 - 1/2015)`
`=8056/2015`
\(A=4(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2014}-\dfrac{1}{2015}) \)
\(A=4(\dfrac{1}{1}-\dfrac{1}{2015}) \)
\(A=4.\dfrac{4}{2015} \)
\(A=\dfrac{8056}{2015} \)
Giải:
\(A=\dfrac{4}{1.2}+\dfrac{4}{2.3}+\dfrac{4}{3.4}+...+\dfrac{4}{2014.2015}\)
\(A=4.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2014.2015}\right)\)
\(A=4.\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2014}-\dfrac{1}{2015}\right)\)
\(A=4.\left(\dfrac{1}{1}-\dfrac{1}{2015}\right)\)
\(A=4.\dfrac{2014}{2015}\)
\(A=\dfrac{8056}{2015}\)
