1,Tính:
1 và 1/15 x 1 và 1/16 x 1và 1/17 x ... 1 và 1/2006
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\(1\frac{1}{15}\cdot1\frac{1}{16}\cdot1\frac{1}{17}\cdot...\cdot1\frac{1}{2006}\)
\(=\frac{16}{15}\cdot\frac{17}{16}\cdot\frac{18}{17}\cdot...\cdot\frac{2007}{2006}\)
\(=\frac{16\cdot17\cdot18\cdot...\cdot2007}{15\cdot16\cdot17\cdot...\cdot2006}\)
\(=\frac{2007}{15}\)
1\(\frac{1}{15}\) x 1\(\frac{1}{16}\) x 1\(\frac{1}{17}\) x ............ x 1\(\frac{1}{2016}\)
= \(\frac{16}{15}\)x \(\frac{17}{16}\)x \(\frac{18}{17}\)x ................. x \(\frac{2017}{2016}\)
= \(\frac{1}{15}\)x 2017
= \(\frac{2017}{15}\)
1. 2006/987654321 + 2007/246813579 = 2007/246813579 + 2006/987654321
=>
2.
3 - (5.3/8 + X - 7 . 5/24) : 6 . 2/3 =2
3 - (15/8 + X - 35/24) : 4 = 2
3 - (15/8 + X - 35/24) = 2 . 4
3 - (15/8 + X - 35/24) = 8
15/8 + X - 35/24 = 3 - 8
15/8 + X - 35/24 = -5
15/8 + X = -5 + 35/24
15/8 + X = -85/24
X = -85/24 - 15/8
X = -65/12
Vậy X = \(1\frac{1}{5}\times1\frac{1}{6}\times....\times1\frac{1}{2014}=\frac{6}{5}\times\frac{7}{6}\times....\times\frac{2015}{2014}\)
\(X=\frac{\left(6\times7\times8\times....\times2014\right)\times2015}{\left(6\times7\times8\times....\times2014\right)\times5}\)
\(X=\frac{2015}{5}=403\)
\(\left(-1\frac{1}{15}\right).\left(-1\frac{1}{16}\right).\left(-1\frac{1}{17}\right).........\left(-1\frac{1}{1994}\right)\)
de the nay a dug cho 1 lik e dj
\(=\left(-\frac{16}{15}\right)\left(-\frac{17}{16}\right).....\left(-\frac{1995}{1994}\right)\)
\(=\frac{\left[\left(-16\right)\left(-17\right)....\left(-1994\right)\right]1995}{\left[16.17.....1994\right].15}=\frac{-1995}{15}=-133\)
\(1\dfrac{1}{15}\times1\dfrac{1}{16}\times1\dfrac{1}{17}\times...\times1\dfrac{1}{2006}\\ =\dfrac{16}{15}\times\dfrac{17}{16}\times\dfrac{18}{17}\times...\times\dfrac{2007}{2006}\\ =\dfrac{2007}{15}\\ =\dfrac{669}{5}\)
tại sao bằng 2007/15 ạ?