\(1\dfrac{1}{15}\times1\dfrac{1}{16}\times1\dfrac{1}{17}\times...\times1\dfrac{1}{2006}\\ =\dfrac{16}{15}\times\dfrac{17}{16}\times\dfrac{18}{17}\times...\times\dfrac{2007}{2006}\\ =\dfrac{2007}{15}\\ =\dfrac{669}{5}\)

tại sao bằng 2007/15 ạ?

Đọc đề khó hiểu quá bạn. Chữ "và" ở đây nghĩa là gì nhỉ?

\(1\frac{1}{15}\cdot1\frac{1}{16}\cdot1\frac{1}{17}\cdot...\cdot1\frac{1}{2006}\)

\(=\frac{16}{15}\cdot\frac{17}{16}\cdot\frac{18}{17}\cdot...\cdot\frac{2007}{2006}\)

\(=\frac{16\cdot17\cdot18\cdot...\cdot2007}{15\cdot16\cdot17\cdot...\cdot2006}\)

\(=\frac{2007}{15}\)

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

= \(\frac{2017}{15}\)

\(\left(-1\frac{1}{15}\right).\left(-1\frac{1}{16}\right).\left(-1\frac{1}{17}\right).........\left(-1\frac{1}{1994}\right)\)

de the nay a dug cho 1 lik e dj

\(=\left(-\frac{16}{15}\right)\left(-\frac{17}{16}\right).....\left(-\frac{1995}{1994}\right)\)

\(=\frac{\left[\left(-16\right)\left(-17\right)....\left(-1994\right)\right]1995}{\left[16.17.....1994\right].15}=\frac{-1995}{15}=-133\)

a)    \(\frac{3}{16}+\frac{4}{15}+\frac{5}{16}+\frac{1}{15}\)

\(=\left(\frac{3}{16}+\frac{5}{16}\right)+\left(\frac{4}{15}+\frac{1}{15}\right)\)

\(=\frac{1}{2}+\frac{1}{3}\)

\(=\frac{5}{6}\)

b)   \(\frac{6}{7}\times\frac{8}{15}\times\frac{7}{6}\times\frac{15}{16}\)

\(=\left(\frac{6}{7}\times\frac{7}{6}\right)\times\left(\frac{8}{15}\times\frac{15}{16}\right)\)

\(=1\times\frac{1}{2}=\frac{1}{2}\)

c)   \(\frac{19}{20}\times\frac{13}{21}+\frac{9}{20}\times\frac{8}{21}\)

\(=\frac{19\times13}{20\times21}+\frac{9\times8}{20\times21}\)

\(=\frac{247}{420}+\frac{72}{420}\)

\(=\frac{319}{420}\)

còn phần D đâu bn 

tích cho chị nha

 câu a)     = 5/6

 câu b = 1/2

 câu c = 319/420

a)=(3/8+10/16)+(7/12+10/24)

=1+1=2

c)=(4/6+14/6)+(7/13+19/13)+(17/9+1/9)

=3+2+2=7