Tính: A= 1- $\frac{5}{6}$ + $\frac{7}{12}$ – $\frac{9}{20}$ + $\frac{11}{30}$ – $\frac{13}{42}$ + $\frac{15}{56}$ -$\frac{17}{72}$ + $\frac{19}{90}$

0 bình luận về “Tính: A= 1- $\frac{5}{6}$ + $\frac{7}{12}$ – $\frac{9}{20}$ + $\frac{11}{30}$ – $\frac{13}{42}$ + $\frac{15}{56}$ -$\frac{17}{72}$ + $\frac{19}{90}$”

1. Đáp án: $A = \dfrac{2}{5}$

    

   Giải thích các bước giải:

   $\begin{array}{l}
   A = 1 – \dfrac{5}{6} + \dfrac{7}{{12}} – \dfrac{9}{{20}} + \dfrac{{11}}{{30}}\\
    – \dfrac{{13}}{{42}} + \dfrac{{15}}{{56}} – \dfrac{{17}}{{72}} + \dfrac{{19}}{{90}}\\
    = 1 – \dfrac{{2 + 3}}{{2.3}} + \dfrac{{3 + 4}}{{3.4}} – \dfrac{{4 + 5}}{{4.5}} + \dfrac{{5 + 6}}{{5.6}}\\
    – \dfrac{{6 + 7}}{{6.7}} + \dfrac{{7 + 8}}{{7.8}} – \dfrac{{8 + 9}}{{8.9}} + \dfrac{{9.10}}{{9.10}}\\
    = 1 – \dfrac{1}{2} – \dfrac{1}{3} + \dfrac{1}{3} + \dfrac{1}{4} – \dfrac{1}{4} – \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{6}\\
    – \dfrac{1}{6} – \dfrac{1}{7} + \dfrac{1}{7} + \dfrac{1}{8} – \dfrac{1}{8} – \dfrac{1}{9} + \dfrac{1}{9} + \dfrac{1}{{10}}\\
    = 1 – \dfrac{1}{2} + \dfrac{1}{{10}}\\
    = \dfrac{1}{2} – \dfrac{1}{{10}}\\
    = \dfrac{4}{{10}} = \dfrac{2}{5}
   \end{array}$

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