Đáp án:

 F=1/1.1985+1/2.1986+1/3.1987+.........+1/16.2000

1984F=1984/1.1985+1984/2.1986+1984/3.1987+...............+1984/16.2000

1984F=1-1985+1/2-1/1986+1/3-1/1987+...........+1/16-1/2000

1984F=1-1/2000

1984F= 1999/2000

F=1999/3968000

Mong bn ủng hộ Mik !! xin cảm ơn bn !! Bn HT !!

nha bạn :))))))))))))))))))

1/1.1985+1/2.1986+1/3.1987+.........+1/16.2000

1984F=1984/1.1985+1984/2.1986+1984/3.1987+...............+1984/16.2000

1984F=1-1985+1/2-1/1986+1/3-1/1987+...........+1/16-1/2000

1984F=1-1/2000

1984F= 1999/2000

1999/3968000

2, \(\frac{1}{1.1985}+\frac{1}{2.1986}+\frac{1}{3.1987}+...+\frac{1}{16.2000}\)

\(=\frac{1984}{1.1985}+\frac{1984}{2.1986}+\frac{1984}{3.1987}+...+\frac{1984}{16.2000}\)

\(=\frac{1}{1}-\frac{1}{1985}+\frac{1}{2}-\frac{1}{1986}+\frac{1}{3}-\frac{1}{1987}+...+\frac{1}{16}-\frac{1}{2000}\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{16}\right)-\left(\frac{1}{1985}+\frac{1}{1986}+...+\frac{1}{2000}\right)\)

Đến đây không tính được nữa nhé.

đặt F=1/1.1985+1/2.1986+1/3.1987+.........+1/16.2000

1984F=1984/1.1985+1984/2.1986+1984/3.1987+...............+1984/16.2000

1984F=1-1985+1/2-1/1986+1/3-1/1987+...........+1/16-1/2000

1984F=1-1/2000

1984F= 1999/2000

F=1999/3968000

-3x = 4y; 6y = 7z và x - 2y + 3z = -48
=> x=-84
y=63
z=54

nha bạn chúc bạn học tốt nha 

-3x = 4y ; 6y = 7z và x - 2y + 3z = 48

=> x = -84 

     y = 63

     z = 54

-HT-

X=-2

chúc bn học tốt

bạn có thể làm cụ thể hơn đc ko !

=1/2014-(1/2014.2013+1/2013.2012+...+1/3.2+1/2.1)

=1/2014-(1/-1/2+1/2-1/3+...+1/2013-1/2014)

=1/2014-1+1/2014

=-1006/1007

Lm ra luôn, ko cần ghi đề nhá !!!

\(=\frac{1}{2014}-\frac{2014-2013}{2014.2013}-\frac{2013-2012}{2013.2012}-...-\frac{3-2}{3.2}-\frac{2-1}{2.1}\)

\(=\frac{1}{2014}-\left(\frac{2014}{2014.2013}-\frac{2013}{2014.2013}\right)-...-\left(\frac{3}{3.2}-\frac{2}{3.2}\right)-\left(\frac{2}{2.1}-\frac{1}{2.1}\right)\)

\(=\frac{1}{2014}+\left(\frac{1}{2014}-\frac{1}{2013}\right)+...+\left(\frac{1}{3}-\frac{1}{2}\right)+\left(\frac{1}{2}-1\right)\)

\(=\frac{1}{2007}-1\)

\(=\frac{-1006}{1007}\)

 \(\frac{3}{7}+\frac{5}{3\cdot7}+\frac{7}{3\cdot19}+\frac{9}{7\cdot19}\)

\(=\frac{3}{7}+\frac{5}{7\cdot3}+\frac{7}{3\cdot19}+\frac{9}{19\cdot7}\)

\(=4\left(\frac{3}{4\cdot7}+\frac{5}{7\cdot12}+\frac{7}{12\cdot19}+\frac{9}{19\cdot28}\right)\)

\(=4\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{19}+\frac{1}{19}-\frac{1}{28}\right)\)

\(=4\left(\frac{1}{4}-\frac{1}{28}\right)\)

\(=4\cdot\frac{3}{14}\)

\(=\frac{12}{14}=\frac{6}{7}\)

Trả lời :

\(\frac{3}{7}+\frac{5}{7}+\frac{7}{3.19}+\frac{9}{7.19}\)

\(=\frac{3}{7}+\frac{5}{7}+\frac{7}{57}+\frac{9}{133}\)

\(=\left(\frac{3}{7}+\frac{5}{7}\right)+\frac{7}{57}+\frac{9}{133}\)

\(=\frac{8}{7}+\frac{5}{57}+\frac{9}{133}\)

... 

Tự quy đồng

~HT~

=\(\frac{2.2.6}{2.2}+\frac{2.10}{2.13}+\frac{3.4}{13.4}+\frac{4.3}{13.4}\)\(+\frac{2.4}{4.2.9}+\frac{2.20}{9.2.7}\)

= \(6+\frac{10}{13}+\frac{3}{13}+\frac{1}{9}+\frac{20}{63}\)

= 6 +1+3/7

=52/7

Giúp tôi giải bài toán này nha

Cộng vế với vế ta có:

\(x\left(x+y+z\right)+y\left(x+y+z\right)+z\left(x+y+z\right)=9\)

\(\Leftrightarrow\left(x+y+z\right)\left(x+y+z\right)=9\)

\(\Leftrightarrow\left(x+y+z\right)^2=3^2\Leftrightarrow\orbr{\begin{cases}x+y+z=3\\x+y+z=-3\end{cases}}\)

+) thay x+y+z=3 vào đề bài ta có:

\(\hept{\begin{cases}3x=-5\\3y=9\\3z=5\end{cases}\Leftrightarrow\hept{\begin{cases}x=\frac{-5}{3}\\y=3\\z=\frac{5}{3}\end{cases}}}\)

+) thay x+y+z=-3 vào đề bài ta có:

\(\hept{\begin{cases}-3x=-5\\-3y=9\\-3z=5\end{cases}\Leftrightarrow\hept{\begin{cases}x=\frac{5}{3}\\y=-3\\z=-\frac{5}{3}\end{cases}}}\)

Vậy....