Ta quy về dạng tổng quát xét cho dễ nhé.

\(\dfrac{1}{x\cdot\left(x+2\right)}=\dfrac{1}{2}.\dfrac{2}{x.\left(x+2\right)}=\dfrac{1}{2}.\left(\dfrac{1}{x}-\dfrac{1}{x-2}\right)\)

Từ đó áp dụng dạng tổng quát để rút gọn là ra.

Chúc em học tốt!

10,82896825 :V

a. x = 1+ 2+ 3+ 4 + 5 + 6 + 7 + 8 + 9 +10

       = (1 +10) + (2+9) + ( 3 +8 ) + (4 + 7 ) + (5 + 6)

       = 11 +11 + 11+ 11 +11

       = 11 x 5

       = 55

b. y = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20

      = (2+20) + (4 + 18) + (6 + 16) +(8 + 14) + (10 +12)

       = 22 + 22 + 22 +22 + 22

       = 22 x 5

       = 110

a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)

= (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + \(\dfrac{8}{1}\)

= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8

=  1 + 1 + 8

=  2 + 8

= 10

b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{10}{20}\)

=  \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (\(\dfrac{2}{2}\) + \(\dfrac{3}{3}\) + \(\dfrac{4}{4}\) + \(\dfrac{5}{5}\)+ \(\dfrac{6}{6}+\dfrac{7}{7}+\dfrac{8}{8}\) + \(\dfrac{10}{10}\))

= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (1 + 1 +1 + 1+ 1+ 1+ 1 +1)

= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x 1 x 8

= \(\dfrac{1}{2}\) + \(\)\(\dfrac{1}{2}\) x 8

= \(\dfrac{1}{2}\) + 4

= \(\dfrac{9}{2}\) 

a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)

  = (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + 8

= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8

= 1 + 1 + 8

= 2 + 8

= 10

b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{9}{18}\) + \(\dfrac{10}{20}\)

= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\)

= \(\dfrac{1}{2}\) x 10

= 5

1: =72/90+65/90=137/90

2: =24/56-77/56=-53/56

3: =-7/10+4/5=1/10

4: =15/100-4/100=11/100

5: =4/6-5/6=-1/6

6: =10/40-15/40-76/40=-81/40

7: =-9/10+7/18

=-81/90+35/90=-46/90=-23/45

8: =27/90-55/90=-28/90=-14/45

9: =36/60-50/60-35/60=-49/60

10: =-4/9+5/6-3/8

=-32/72+60/72-27/72

=1/72

\(A=\frac{5}{2.4.6}+\frac{5}{4.6.8}+...+\frac{5}{16.18.20}\)

\(4A=5.\left(\frac{4}{2.4.6}+\frac{4}{4.6.8}+...+\frac{4}{16.18.20}\right)\)

\(4A=5.\left(\frac{1}{2.4}-\frac{1}{4.6}+\frac{1}{4.6}-\frac{1}{6.8}+...+\frac{1}{16.18}-\frac{1}{18.20}\right)\)

\(4A=5.\left(\frac{1}{8}-\frac{1}{360}\right)\)

\(4A=5.\left(\frac{45}{360}-\frac{1}{360}\right)\)

\(4A=5.\frac{44}{360}\)

\(A=\frac{5.44}{360.4}\)

\(A=\frac{11}{72}\)

Tham khảo~

\(A=\frac{5}{2\cdot4\cdot6}+\frac{5}{4\cdot6\cdot8}+.....+\frac{5}{16\cdot18\cdot20}\)

\(\frac{4}{5}A=\frac{4}{2\cdot4\cdot6}+\frac{4}{4\cdot6\cdot8}+.........+\frac{4}{16\cdot18\cdot20}\)

\(\frac{4}{5}A=\frac{1}{2\cdot4}-\frac{1}{4\cdot6}+\frac{1}{4\cdot6}-\frac{1}{6\cdot8}+.........+\frac{1}{16\cdot18}-\frac{1}{18\cdot20}\)

\(\frac{4}{5}A=\frac{1}{2\cdot4}-\frac{1}{18\cdot20}\)

\(\frac{4}{5}A=\frac{1}{8}-\frac{1}{360}\)

\(\frac{4}{5}A=\frac{11}{90}\)

\(A=\frac{11}{90}:\frac{4}{5}=\frac{11}{72}\)

= 1/2 x 5 = 5/2

= 270 nha bạn

1+1+2+2+3+3+4+4+5+5+6+6+7+7+8+8+9+9=2+4+6+8+10+12+14+16+18

                                                                        =(2+8)+(4+6)+10+(12+18)+(14+16)

                                                                        =10+10+10+30+30

                                                                        =30+30+30

                                                                        =30x3

                                                                        =90

Bạn vào:câu hỏi của :Vũ Ngân Hà -olm

\(A=\frac{1\cdot2+2\cdot4+3\cdot6+4\cdot8+5\cdot10+6\cdot12}{3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20+18\cdot24}\)

\(A=\frac{2\cdot3\left[1\cdot2\right]+2\cdot3\left[2\cdot4\right]+2\cdot3\left[3\cdot6\right]+2\cdot3\left[4\cdot8\right]+2\cdot3\left[5\cdot10\right]}{3\cdot4\left[3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20\right]}\)

\(A=\frac{\left[3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20\right]}{2\cdot3\left[3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20\right]}=\frac{1}{2\cdot3}=\frac{1}{6}\)