Đáp án + Giải thích các bước giải :

2/3 + 14/15 + 34/35 + 62/63 + 98/90 + 142/143 + 194/195

= ( 2/3 + 14/15 ) + ( 34/35 + 62/63 ) + ( 98/90 + 142/143 ) + 194/195

= 8/5 + 88/45 + 13397/6435 + 194/195

= ( 8/5 + 88/45 ) + ( 13397/6435 + 194/195 )

= 32/9 + 1523/495

= 3283/495

NO COPY
@mai

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\begin{array}{l} A = \dfrac{2}{3} + \dfrac{{14}}{{15}} + \dfrac{{34}}{{35}} + \dfrac{{62}}{{63}} + \dfrac{{98}}{{99}} + \dfrac{{142}}{{143}} + \dfrac{{194}}{{195}}\\ = \left( {1 - \dfrac{1}{3}} \right) + \left( {1 - \dfrac{1}{{15}}} \right) + \left( {1 - \dfrac{1}{{35}}} \right) + \left( {1 - \dfrac{1}{{63}}} \right) + \left( {1 - \dfrac{1}{{99}}} \right) + \left( {1 - \dfrac{1}{{143}}} \right) + \left( {1 - \dfrac{1}{{195}}} \right)\\ = 7 - \left( {\dfrac{1}{3} + \dfrac{1}{{15}} + \dfrac{1}{{35}} + \dfrac{1}{{63}} + \dfrac{1}{{99}} + \dfrac{1}{{143}} + \dfrac{1}{{195}}} \right)\\ = 7 - \left( {\dfrac{1}{{1.3}} + \dfrac{1}{{3.5}} + \dfrac{1}{{5.7}} + \dfrac{1}{{7.9}} + \dfrac{1}{{9.11}} + \dfrac{1}{{11.13}} + \dfrac{1}{{13.15}}} \right)\\ = 7 - \dfrac{1}{2}\left( {\dfrac{2}{{1.3}} + \dfrac{2}{{3.5}} + \dfrac{2}{{5.7}} + \dfrac{2}{{7.9}} + \dfrac{2}{{9.11}} + \dfrac{2}{{11.13}} + \dfrac{2}{{13.15}}} \right)\\ = 7 - \dfrac{1}{2}\left( {\dfrac{1}{1} - \dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{5} + \dfrac{1}{5} - \dfrac{1}{7} + \dfrac{1}{7} - \dfrac{1}{9} + \dfrac{1}{9} - \dfrac{1}{{11}} + \dfrac{1}{{11}} - \dfrac{1}{{13}} + \dfrac{1}{{13}} - \dfrac{1}{{15}}} \right)\\ = 7 - \dfrac{1}{2}\left( {1 - \dfrac{1}{{15}}} \right)\\ = 7 - \dfrac{7}{{15}}\\ = \dfrac{{98}}{{15}} \end{array}