Câu hỏi của Hoàng Thu Trang

Question

$\frac{2006}{1.2}$+$\frac{2006}{2.3}$+...+$\frac{2006}{2006.2007}$

Momozono Nanami · Accepted Answer

$\frac{2006}{1.2}+\frac{2006}{2.3}+...+\frac{2006}{2006.2007}$

$=2006.\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2006.2007}\right)$

$=2006.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2006}-\frac{1}{2007}\right)$

$=2006.\left(1-\frac{1}{2007}\right)$

$=2006.\frac{2006}{2007}$

$=\frac{2006^2}{2007}$

Câu trả lời:

$\frac{2006}{1.2}+\frac{2006}{2.3}+...+\frac{2006}{2006.2007}$

$=2006.\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2006.2007}\right)$

$=2006.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2006}-\frac{1}{2007}\right)$

$=2006.\left(1-\frac{1}{2007}\right)$

$=2006.\frac{2006}{2007}$

$=\frac{2006^2}{2007}$

Hiếu Lê · Answer

$=\frac{2006}{1.2}+\frac{2006}{2.3}+...+\frac{2006}{2006.2007}$

$=2006 \left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2006.2007}\right)$

$=2006.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2006}-\frac{1}{2007}\right)$

$=2006.\left(1-\frac{1}{2007}\right)$

$=2006.\frac{2006}{2007}=\frac{4024036}{2007}$

Câu trả lời:

$=\frac{2006}{1.2}+\frac{2006}{2.3}+...+\frac{2006}{2006.2007}$

$=2006 \left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2006.2007}\right)$

$=2006.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2006}-\frac{1}{2007}\right)$

$=2006.\left(1-\frac{1}{2007}\right)$

$=2006.\frac{2006}{2007}=\frac{4024036}{2007}$