\(A=\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+\frac{2}{11\cdot13}+\frac{2}{13\cdot15}\)

\(A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{13}-\frac{1}{15}=1-\frac{1}{15}=\frac{14}{15}\)

Bài làm:

Ta có: \(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\)

\(A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\)

\(A=1-\frac{1}{15}\)

\(A=\frac{14}{15}\)

\(a,\frac{-1}{9}.\frac{15}{22}.\frac{-9}{25}\)

\(=\frac{-1.15.\left(-9\right)}{9.22.25}\)

\(=\frac{3}{110}\)

\(b,\frac{-2}{7}.\left(\frac{5}{13}-\frac{9}{15}\right)-\frac{2}{7}.\frac{8}{13}\)

\(=\frac{-2}{7}.\left(\frac{5}{13}+\frac{8}{13}-\frac{3}{5}\right)\)

\(=\frac{-2}{7}.\left(1-\frac{3}{5}\right)\)

\(=\frac{-2}{7}.\frac{2}{5}\)

\(=\frac{-4}{35}\)

\(c,\frac{3}{10}.\left(\frac{-4}{9}+\frac{2}{5}\right)-\frac{3}{10}.\left(\frac{5}{9}-\frac{3}{5}\right)\)

\(=\frac{3}{10}.\left[\left(\frac{-4}{9}+\frac{2}{5}\right)-\left(\frac{5}{9}-\frac{3}{5}\right)\right]\)

\(=\frac{3}{10}.\left(\frac{-4}{9}+\frac{2}{5}-\frac{5}{9}+\frac{3}{5}\right)\)

\(=\frac{3}{10}.\left[\left(\frac{-4}{9}-\frac{5}{9}\right)+\left(\frac{2}{5}+\frac{3}{5}\right)\right]\)

\(=\frac{3}{10}.\left(-1+1\right)\)

\(=\frac{3}{10}.0\)

\(=0\)

\(d,\frac{4}{11}-\frac{5}{13}+\frac{7}{11}-\frac{8}{13}\)

\(=\left(\frac{4}{11}+\frac{7}{11}\right)+\left(\frac{-5}{13}-\frac{8}{13}\right)\)

\(=1-1\)

\(=0\)

Học tốt

a: =-5/9-4/9+8/15+7/15-2/11=-2/11

b: =10/17+7/17-5/13-8/13+11/25

=11/25

c: =(9/12-2/12)*3/2=7/12*3/2=21/24=7/8

d: =(31/10-25/10)*3-2

=3/5*3-2

=9/5-2

=-1/5

a) \(\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}-\dfrac{3}{4}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{72}\)

\(=\dfrac{5+9+1}{15}-\dfrac{27+8+1}{36}+\dfrac{1}{72}=1-1+\dfrac{1}{72}=\dfrac{1}{72}\)

b) \(=\dfrac{1}{5}-\dfrac{1}{5}-\dfrac{3}{7}+\dfrac{3}{7}+\dfrac{5}{9}-\dfrac{5}{9}-\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{7}{13}-\dfrac{7}{13}-\dfrac{9}{16}\)

\(=\dfrac{9}{16}\)

Gọi tổng trên là A

Đề sai rồi đề đúng đây : A = 2/3.5 + 2/5.7 + 2/7.9 + 2/9.11 + 2/11.13 + 2/13.15

A = 1/3 - 1/5 + 1/5 - 1/7 +........+ 1/13 - 1/15

A = 1/3 - 1/15

A = 4/15

có câu tương tự đó bn

Bài 1: 

\(=\dfrac{-1}{2}+\dfrac{3}{5}-\dfrac{1}{9}+\dfrac{1}{131}+\dfrac{2}{7}+\dfrac{4}{35}-\dfrac{7}{18}\)

\(=\left(-\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{7}{18}\right)+\left(\dfrac{3}{5}+\dfrac{2}{7}+\dfrac{4}{35}\right)+\dfrac{1}{131}\)

\(=\dfrac{-9-2-7}{18}+\dfrac{21+10+4}{35}+\dfrac{1}{131}\)

=1/131

Bài 2:

b: \(B=\dfrac{1}{99}-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{98\cdot99}\right)\)

\(=\dfrac{1}{99}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{98}-\dfrac{1}{99}\right)\)

\(=\dfrac{1}{99}-\dfrac{98}{99}=-\dfrac{97}{99}\)

`1/3-5/6+3/2`

`=2/6-5/6+9/6`

`=-3/6+9/6`

`=6/6`

`=1`

__

`2/13-(15/13+4-0,5)`

`=2/13-1513-4+0,5`

`=(2/13-15/13)-4,5`

`=-13/13-4,5`

`=-1-4,5`

`=-5,5`

__

`-(1/9+7/5-3/11)+(-2/5+17/9-8/11)`

`=-1/9-7/5+3/11+(-2)/5+17/9-8/11`

`=(-1/9+17/9)+(-7/5+(-2)/5)+(3/11-8/11)`

`=16/9-9/5-5/11`

`=-236/495`

__

`5,75-3,25+5 5/6`

`=5/2+35/6`

`=15/6+35/6`

`=50/6`

`=25/3`

  \(\dfrac{1}{2}+\dfrac{3}{4}-\left(\dfrac{3}{4}-\dfrac{4}{5}\right)\)

=\(\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{3}{4}+\dfrac{4}{5}\)

=\(\left(\dfrac{1}{2}+\dfrac{4}{5}\right)+\left(\dfrac{3}{4}-\dfrac{3}{4}\right)\) 

=\(\left(\dfrac{5}{10}+\dfrac{8}{10}\right)+0\)

=\(\dfrac{13}{10}\)

\(-\dfrac{7}{25}.\dfrac{11}{13}+\left(-\dfrac{7}{25}\right).\dfrac{2}{13}-\dfrac{18}{25}\)

=\(-\dfrac{7}{25}.\cdot\left(\dfrac{11}{13}+\dfrac{2}{13}\right)-\dfrac{18}{25}\) 

=\(-\dfrac{7}{25}.1-\dfrac{18}{25}\) 

=\(-\dfrac{7}{25}-\dfrac{18}{25}\) 

=\(-\dfrac{25}{25}\) = \(-1\)

(-3,2) +\(\dfrac{15}{64}+\left(0.8-2\dfrac{4}{15}\right):3\dfrac{2}{3}\) 

=\(-\dfrac{16}{5}+\dfrac{15}{64}+(\dfrac{4}{5}-\dfrac{34}{15}):\dfrac{11}{3}\)

=\(-\dfrac{16}{5}+\dfrac{15}{64}+(-\dfrac{22}{5}):\dfrac{11}{3}\)

=\(-\dfrac{16}{5}+\dfrac{15}{64}+\dfrac{-2}{5}\)

=(\(-\dfrac{16}{5}+\dfrac{-2}{5}\)) +\(\dfrac{15}{64}\)

=\(-\dfrac{18}{5}+\dfrac{15}{64}\)

\(-\dfrac{1152}{320}+\dfrac{75}{320}\)

\(-\dfrac{1077}{320}\)