Toán $\color{black}{A = \frac{1}{1.2.3} + \frac{1}{3.4.5} + …. + \frac{1}{10.11.12}}$ 09/09/2021 By Valentina $\color{black}{A = \frac{1}{1.2.3} + \frac{1}{3.4.5} + …. + \frac{1}{10.11.12}}$
$A=\dfrac{1}{1.2.3}+\dfrac{1}{3.4.5}+\dfrac{1}{4.5.6}+…+\dfrac{1}{10.11.12}\\A=\dfrac{1}{2}\left ( \dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+\dfrac{1}{4.5}-\dfrac{1}{5.6}+…+\dfrac{1}{10.11}-\dfrac{1}{11.12} \right )\\A=\dfrac{1}{2}\left ( \dfrac{1}{1.2}-\dfrac{1}{11.12} \right )\\A=\dfrac{1}{2}\left ( \dfrac{1}{2}-\dfrac{1}{132}\right )\\A=\dfrac{1}{2}.\dfrac{65}{132}=\dfrac{65}{264}$ Trả lời
Đáp án: A=65/264 Giải thích các bước giải: A= 1/1.2.3+1/3.4.5+…….+1/10.11.12 A=1/2.(2/1.2.3+2/3.4.5+…..+1/10.11.12) A=1/2(1/1.2-1/2.3+1/3.4-1/4.5+……….+1/10.11-1/11.12) A=1/4-1/264( cái này triệt tiêu rồi nhân cho 1/2 mình làm tắt) A=65/264 Trả lời
$A=\dfrac{1}{1.2.3}+\dfrac{1}{3.4.5}+\dfrac{1}{4.5.6}+…+\dfrac{1}{10.11.12}\\A=\dfrac{1}{2}\left ( \dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+\dfrac{1}{4.5}-\dfrac{1}{5.6}+…+\dfrac{1}{10.11}-\dfrac{1}{11.12} \right )\\A=\dfrac{1}{2}\left ( \dfrac{1}{1.2}-\dfrac{1}{11.12} \right )\\A=\dfrac{1}{2}\left ( \dfrac{1}{2}-\dfrac{1}{132}\right )\\A=\dfrac{1}{2}.\dfrac{65}{132}=\dfrac{65}{264}$
Đáp án: A=65/264
Giải thích các bước giải:
A= 1/1.2.3+1/3.4.5+…….+1/10.11.12
A=1/2.(2/1.2.3+2/3.4.5+…..+1/10.11.12)
A=1/2(1/1.2-1/2.3+1/3.4-1/4.5+……….+1/10.11-1/11.12)
A=1/4-1/264( cái này triệt tiêu rồi nhân cho 1/2 mình làm tắt)
A=65/264