Tính hợp lí tổng sau: -3/4.8/9.15/16….. .899/900 18/09/2021 Bởi Ariana Tính hợp lí tổng sau: -3/4.8/9.15/16….. .899/900
Đáp án + Giải thích các bước giải: `3/4 . 8/9 . 15/16 …. 899/900` `=(3.8.15…899)/(4.9.16…900)=(1.3.2.4.3.5…29.31)/(2.2.3.3.4.4…30.30)` `=(1.2.3…29)/(2.3.4…30) . (3.4.5…31)/(2.3.4…30)=1/30 . 31/2=31/60` Bình luận
$\begin{array}{l}\quad\dfrac34\cdot\dfrac89\cdot\dfrac{15}{16}\cdots\dfrac{899}{900}\\=\dfrac{1.3}{2^2}\cdot\dfrac{2.4}{3^2}\cdot\dfrac{3.5}{4^2}\cdots\dfrac{29.31}{30^2}\\=\dfrac{1.3.2.4.3.5.4.6\dots27.29.28.30.29.31}{2^2.3^2.4^2\dots30^2}\\=\dfrac{1.2.3^2.4^2.5^2\dots29^2.30.31}{2^2.3^2.4^2\dots29^2.30^2}\\=\dfrac{1.31}{2.30}\\=\dfrac{31}{60} \end{array}$ Bình luận
Đáp án + Giải thích các bước giải:
`3/4 . 8/9 . 15/16 …. 899/900`
`=(3.8.15…899)/(4.9.16…900)=(1.3.2.4.3.5…29.31)/(2.2.3.3.4.4…30.30)`
`=(1.2.3…29)/(2.3.4…30) . (3.4.5…31)/(2.3.4…30)=1/30 . 31/2=31/60`
$\begin{array}{l}\quad\dfrac34\cdot\dfrac89\cdot\dfrac{15}{16}\cdots\dfrac{899}{900}\\=\dfrac{1.3}{2^2}\cdot\dfrac{2.4}{3^2}\cdot\dfrac{3.5}{4^2}\cdots\dfrac{29.31}{30^2}\\=\dfrac{1.3.2.4.3.5.4.6\dots27.29.28.30.29.31}{2^2.3^2.4^2\dots30^2}\\=\dfrac{1.2.3^2.4^2.5^2\dots29^2.30.31}{2^2.3^2.4^2\dots29^2.30^2}\\=\dfrac{1.31}{2.30}\\=\dfrac{31}{60} \end{array}$