Cho biểu thức A =4/1.2+ 4/2.3 + 4/3.4 + ... + 4/2014.2015. Tính A
Giải thích
Ta có \(A = \frac{4}{{1.2}} + \frac{4}{{2.3}} + \frac{4}{{3.4}} + ... + \frac{4}{{2014.2015}}\)
\[ = 4\,\,.\,\,\left( {\frac{1}{{1\,.\,2}} + \frac{1}{{2\,.\,3}} + \frac{1}{{3\,.\,4}} + ... + \frac{1}{{2014\,.\,2015}}} \right)\]
\( = 4.\left( {1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + ... + \frac{1}{{2014}} - \frac{1}{{2015}}} \right)\)
\( = 4\,\,.\,\,\left( {1 - \frac{1}{{2015}}} \right)\)\( = 4.\frac{{2014}}{{2015}}\)\( = \frac{{8056}}{{2015}}\).
Vậy \(A = \frac{{8056}}{{2015}}\).