Tinh nhanh 11/12 +19/20+29/30+41/42+55/56

2 câu trả lời

Đáp án:

 \(\dfrac{115}{24}\)

Giải thích các bước giải:

\[\begin{array}{l}
\frac{{11}}{{12}} + \frac{{19}}{{20}} + \frac{{29}}{{30}} + \frac{{41}}{{42}} + \frac{{55}}{{56}}\\
 = 1 - \frac{1}{{12}} + 1 - \frac{1}{{20}} + 1 - \frac{1}{{30}} + 1 - \frac{1}{{42}} + 1 - \frac{1}{{56}}\\
 = 5 - \left( {\frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}}} \right)\\
 = 5 - \left( {\frac{1}{3} - \frac{1}{4} + \frac{1}{4} - \frac{1}{5} + \frac{1}{5} - \frac{1}{6} + \frac{1}{6} - \frac{1}{7} + \frac{1}{7} - \frac{1}{8}} \right)\\
 = 5 - \left( {\frac{1}{3} - \frac{1}{8}} \right)\\
 = 5 - \frac{5}{{24}}\\
 = \frac{{115}}{{24}}
\end{array}\]

= (1- $\frac{1}{12}$) + (1- $\frac{1}{20}$) + (1- $\frac{1}{30}$) + (1- $\frac{1}{42}$) + (1 - $\frac{1}{56}$)

= 5 - ($\frac{1}{12}$ + $\frac{1}{20}$ + $\frac{1}{30}$ + $\frac{1}{42}$ + $\frac{1}{56}$)

= 5 -( $\frac{1}{3×4}$ + $\frac{1}{4×5}$ + $\frac{1}{5×6}$ + $\frac{1}{6×7}$ + $\frac{1}{7×8}$)

= 5 - ( $\frac{1}{3}$ - $\frac{1}{4}$+$\frac{1}{5}$ + $\frac{1}{5}$-$\frac{1}{6}$ + $\frac{1}{6}$ - $\frac{1}{7}$ + $\frac{1}{7}$ - $\frac{1}{8}$)

= 5- ($\frac{1}{3}$ - $\frac{1}{8}$)

= 5 - $\frac{5}{24}$

= $\frac{115}{24}$

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