Câu hỏi của embappe

Question

(1/2 - 1)(1/3 - 1)(1/4 - 1) ...( 1 2008 -1)( 1 2009 -1)

456 · Accepted Answer

$\left(\dfrac{1}{2}-1\right).\left(\dfrac{1}{3}-1\right).\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{2008}-1\right).\left(\dfrac{1}{2009}-1\right)$

$=-\dfrac{1}{2}.-\dfrac{2}{3}.-\dfrac{3}{4}...-\dfrac{2007}{2008}.-\dfrac{2008}{2009}$

$=-\left(\dfrac{1.2.3...2007.2008}{2.3.4...2008.2009}\right)$

$=-\dfrac{1}{2009}$

Câu trả lời:

$\left(\dfrac{1}{2}-1\right).\left(\dfrac{1}{3}-1\right).\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{2008}-1\right).\left(\dfrac{1}{2009}-1\right)$

$=-\dfrac{1}{2}.-\dfrac{2}{3}.-\dfrac{3}{4}...-\dfrac{2007}{2008}.-\dfrac{2008}{2009}$

$=-\left(\dfrac{1.2.3...2007.2008}{2.3.4...2008.2009}\right)$

$=-\dfrac{1}{2009}$

Hải Duy Nguyễn · Answer

(21−1).(31−1).(41−1)...(20081−1).(20091−1)

$= - \frac{1}{2} . - \frac{2}{3} . - \frac{3}{4} . . . - \frac{2007}{2008} . - \frac{2008}{2009}$

$= - \left(\right. \frac{1.2.3...2007.2008}{2.3.4...2008.2009} \left.\right)$

$= - \frac{1}{2009}$

Câu trả lời:

(21−1).(31−1).(41−1)...(20081−1).(20091−1)

$= - \frac{1}{2} . - \frac{2}{3} . - \frac{3}{4} . . . - \frac{2007}{2008} . - \frac{2008}{2009}$

$= - \left(\right. \frac{1.2.3...2007.2008}{2.3.4...2008.2009} \left.\right)$

$= - \frac{1}{2009}$

Hải Duy Nguyễn · Answer

(2\1−1).(3\1−1).(4/1−1)...(2008/1−1).(2009/1−1)

$= - \frac{1}{2} . - \frac{2}{3} . - \frac{3}{4} . . . - \frac{2007}{2008} . - \frac{2008}{2009}$

$= - \left(\right. \frac{1.2.3...2007.2008}{2.3.4...2008.2009} \left.\right)$

$= - \frac{1}{2009}$

Câu trả lời:

(2\1−1).(3\1−1).(4/1−1)...(2008/1−1).(2009/1−1)

$= - \frac{1}{2} . - \frac{2}{3} . - \frac{3}{4} . . . - \frac{2007}{2008} . - \frac{2008}{2009}$

$= - \left(\right. \frac{1.2.3...2007.2008}{2.3.4...2008.2009} \left.\right)$

$= - \frac{1}{2009}$