1, tính A= 4/2×5+4/5×8+4/8×11+…..+4/65×68
2, tính B= 2^2/1×3.3^2/2×4.4^2/3×5…..999^2/998×1000
giúp mk với mk đang cần gấp lắm
1, tính A= 4/2×5+4/5×8+4/8×11+…..+4/65×68
2, tính B= 2^2/1×3.3^2/2×4.4^2/3×5…..999^2/998×1000
giúp mk với mk đang cần gấp lắm
Đáp án:
1) `11/17`
2) `999/500`
Giải thích các bước giải:
1) `A = 4/2.5 + 4/5.8 + 4/8.11 +…+ 4/65.68`
`= 4/3 . (3/2.5 + 3/5.8 + 3/8.11+…+ 3/65.68)`
`= 4/3 . (1/2 – 1/5 + 1/5 – 1/8 + 1/8 – 1/11 +…+ 1/65 – 1/68)`
`= 4/3 . (1/2 – 1/68)`
`= 2/3 – 1/51=11/17`
2) `B=2^2/1.3. 3^2/2.4. 4^2/3.5 … 999^2/998.1000`
`=(2.2)/1.3 . (3.3)/2.4 . (4.4)/3.5 … (999.999)/998.1000`
`=((2.3.4…999).(2.3.4…999))/((1.2.3…998).(3.4.5…1000))=(999.2)/1000= 999/500`
Đáp án:
$\begin{array}{l}
A = \dfrac{4}{{2.5}} + \dfrac{4}{{5.8}} + \dfrac{4}{{8.11}} + … + \dfrac{4}{{65.68}}\\
\Rightarrow A = \dfrac{4}{3}.\left( {\dfrac{3}{{2.5}} + \dfrac{3}{{5.8}} + \dfrac{3}{{8.11}} + … + \dfrac{3}{{65.68}}} \right)\\
\Rightarrow A = \dfrac{4}{3}.\left( {\dfrac{1}{2} – \dfrac{1}{5} + \dfrac{1}{5} – \dfrac{1}{8} + … + \dfrac{1}{{65}} – \dfrac{1}{{68}}} \right)\\
\Rightarrow A = \dfrac{4}{3}.\left( {\dfrac{1}{2} – \dfrac{1}{{68}}} \right)\\
\Rightarrow A = \dfrac{4}{3}.\dfrac{{33}}{{68}}\\
\Rightarrow A = \dfrac{{11}}{{17}}\\
B = \dfrac{{{2^2}}}{{1.3}}.\dfrac{{{3^2}}}{{2.4}}.\dfrac{{{4^2}}}{{3.5}}…\dfrac{{{{999}^2}}}{{998.1000}}\\
= \dfrac{{{2^2}{{.3}^2}{{.4}^2}{{…999}^2}}}{{{{1.2.3}^2}{{.4}^2}{{…998}^2}.999.1000}}\\
= \dfrac{{2.999}}{{1000}}\\
= \dfrac{{999}}{{500}}
\end{array}$