$\frac{1}{1.4}+$ $\frac{1}{4.7}+$ $\frac{1}{7.10}+…+$ $\frac{1}{94.97}+$ $\frac{1}{97.100}$
VIẾT PHÂN SỐ GIỐNG MÌNH NHA
$\frac{1}{1.4}+$ $\frac{1}{4.7}+$ $\frac{1}{7.10}+…+$ $\frac{1}{94.97}+$ $\frac{1}{97.100}$
VIẾT PHÂN SỐ GIỐNG MÌNH NHA
`Đặt` `biểu` `thức` `là` `A`
`Ta` `có:`
`A=1/1.4 + 1/4.7 + 1/7.10 + … +1/94.97 + 1/97.100`
`3A=1-1/4+1/4-1/7+1/7-1/10+…+1/94-1/97+1/97-1/100`
`3A=1-1/100`
`3A=99/100`
`A=99/100÷3`
`A=33/100`
Đáp án:
$\begin{array}{l}
\dfrac{1}{{1.4}} + \dfrac{1}{{4.7}} + \dfrac{1}{{7.10}} + … + \dfrac{1}{{94.97}} + \dfrac{1}{{97.100}}\\
= \dfrac{1}{3}.\left( {\dfrac{3}{{1.4}} + \dfrac{3}{{4.7}} + \dfrac{3}{{7.10}} + … + \dfrac{3}{{94.97}} + \dfrac{3}{{97.100}}} \right)\\
= \dfrac{1}{3}.\left( \begin{array}{l}
\dfrac{{4 – 1}}{{1.4}} + \dfrac{{7 – 4}}{{4.7}} + \dfrac{{10 – 7}}{{7.10}} + …\\
+ \dfrac{{97 – 94}}{{94.97}} + \dfrac{{100 – 97}}{{97.100}}
\end{array} \right)\\
= \dfrac{1}{3}.\left( \begin{array}{l}
1 – \dfrac{1}{4} + \dfrac{1}{4} – \dfrac{1}{7} + \dfrac{1}{7} – \dfrac{1}{{10}} + …\\
+ \dfrac{1}{{94}} – \dfrac{1}{{97}} + \dfrac{1}{{97}} – \dfrac{1}{{100}}
\end{array} \right)\\
= \dfrac{1}{3}.\left( {1 – \dfrac{1}{{100}}} \right)\\
= \dfrac{1}{3}.\dfrac{{99}}{{100}}\\
= \dfrac{{33}}{{100}}
\end{array}$