Tinh nhanh 11/12 +19/20+29/30+41/42+55/56 30/08/2021 Bởi Liliana Tinh nhanh 11/12 +19/20+29/30+41/42+55/56
Đáp án: \(\dfrac{115}{24}\) Giải thích các bước giải: \[\begin{array}{l}\frac{{11}}{{12}} + \frac{{19}}{{20}} + \frac{{29}}{{30}} + \frac{{41}}{{42}} + \frac{{55}}{{56}}\\ = 1 – \frac{1}{{12}} + 1 – \frac{1}{{20}} + 1 – \frac{1}{{30}} + 1 – \frac{1}{{42}} + 1 – \frac{1}{{56}}\\ = 5 – \left( {\frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}}} \right)\\ = 5 – \left( {\frac{1}{3} – \frac{1}{4} + \frac{1}{4} – \frac{1}{5} + \frac{1}{5} – \frac{1}{6} + \frac{1}{6} – \frac{1}{7} + \frac{1}{7} – \frac{1}{8}} \right)\\ = 5 – \left( {\frac{1}{3} – \frac{1}{8}} \right)\\ = 5 – \frac{5}{{24}}\\ = \frac{{115}}{{24}}\end{array}\] Bình luận
= (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 – $\frac{5}{24}$ = $\frac{115}{24}$ Bình luận
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 – $\frac{5}{24}$
= $\frac{115}{24}$