2/3+14/15+34/35+62/63+98/90+142/143+194/195 12/08/2021 Bởi Madeline 2/3+14/15+34/35+62/63+98/90+142/143+194/195
Giải thích các bước giải: Bạn xem lại đề đúng bên dưới. Ta có: $\begin{array}{l}A = \dfrac{2}{3} + \dfrac{{14}}{{15}} + \dfrac{{34}}{{35}} + \dfrac{{62}}{{63}} + \dfrac{{98}}{{99}} + \dfrac{{142}}{{143}} + \dfrac{{194}}{{195}}\\ = \left( {1 – \dfrac{1}{3}} \right) + \left( {1 – \dfrac{1}{{15}}} \right) + \left( {1 – \dfrac{1}{{35}}} \right) + \left( {1 – \dfrac{1}{{63}}} \right) + \left( {1 – \dfrac{1}{{99}}} \right) + \left( {1 – \dfrac{1}{{143}}} \right) + \left( {1 – \dfrac{1}{{195}}} \right)\\ = 7 – \left( {\dfrac{1}{3} + \dfrac{1}{{15}} + \dfrac{1}{{35}} + \dfrac{1}{{63}} + \dfrac{1}{{99}} + \dfrac{1}{{143}} + \dfrac{1}{{195}}} \right)\\ = 7 – \left( {\dfrac{1}{{1.3}} + \dfrac{1}{{3.5}} + \dfrac{1}{{5.7}} + \dfrac{1}{{7.9}} + \dfrac{1}{{9.11}} + \dfrac{1}{{11.13}} + \dfrac{1}{{13.15}}} \right)\\ = 7 – \dfrac{1}{2}\left( {\dfrac{2}{{1.3}} + \dfrac{2}{{3.5}} + \dfrac{2}{{5.7}} + \dfrac{2}{{7.9}} + \dfrac{2}{{9.11}} + \dfrac{2}{{11.13}} + \dfrac{2}{{13.15}}} \right)\\ = 7 – \dfrac{1}{2}\left( {\dfrac{1}{1} – \dfrac{1}{3} + \dfrac{1}{3} – \dfrac{1}{5} + \dfrac{1}{5} – \dfrac{1}{7} + \dfrac{1}{7} – \dfrac{1}{9} + \dfrac{1}{9} – \dfrac{1}{{11}} + \dfrac{1}{{11}} – \dfrac{1}{{13}} + \dfrac{1}{{13}} – \dfrac{1}{{15}}} \right)\\ = 7 – \dfrac{1}{2}\left( {1 – \dfrac{1}{{15}}} \right)\\ = 7 – \dfrac{7}{{15}}\\ = \dfrac{{98}}{{15}}\end{array}$ Bình luận
Giải thích các bước giải:
Bạn xem lại đề đúng bên dưới.
Ta có:
$\begin{array}{l}
A = \dfrac{2}{3} + \dfrac{{14}}{{15}} + \dfrac{{34}}{{35}} + \dfrac{{62}}{{63}} + \dfrac{{98}}{{99}} + \dfrac{{142}}{{143}} + \dfrac{{194}}{{195}}\\
= \left( {1 – \dfrac{1}{3}} \right) + \left( {1 – \dfrac{1}{{15}}} \right) + \left( {1 – \dfrac{1}{{35}}} \right) + \left( {1 – \dfrac{1}{{63}}} \right) + \left( {1 – \dfrac{1}{{99}}} \right) + \left( {1 – \dfrac{1}{{143}}} \right) + \left( {1 – \dfrac{1}{{195}}} \right)\\
= 7 – \left( {\dfrac{1}{3} + \dfrac{1}{{15}} + \dfrac{1}{{35}} + \dfrac{1}{{63}} + \dfrac{1}{{99}} + \dfrac{1}{{143}} + \dfrac{1}{{195}}} \right)\\
= 7 – \left( {\dfrac{1}{{1.3}} + \dfrac{1}{{3.5}} + \dfrac{1}{{5.7}} + \dfrac{1}{{7.9}} + \dfrac{1}{{9.11}} + \dfrac{1}{{11.13}} + \dfrac{1}{{13.15}}} \right)\\
= 7 – \dfrac{1}{2}\left( {\dfrac{2}{{1.3}} + \dfrac{2}{{3.5}} + \dfrac{2}{{5.7}} + \dfrac{2}{{7.9}} + \dfrac{2}{{9.11}} + \dfrac{2}{{11.13}} + \dfrac{2}{{13.15}}} \right)\\
= 7 – \dfrac{1}{2}\left( {\dfrac{1}{1} – \dfrac{1}{3} + \dfrac{1}{3} – \dfrac{1}{5} + \dfrac{1}{5} – \dfrac{1}{7} + \dfrac{1}{7} – \dfrac{1}{9} + \dfrac{1}{9} – \dfrac{1}{{11}} + \dfrac{1}{{11}} – \dfrac{1}{{13}} + \dfrac{1}{{13}} – \dfrac{1}{{15}}} \right)\\
= 7 – \dfrac{1}{2}\left( {1 – \dfrac{1}{{15}}} \right)\\
= 7 – \dfrac{7}{{15}}\\
= \dfrac{{98}}{{15}}
\end{array}$
Cho mình xin hay nhất