1/1x2+1/2x3+1/3x4+..+1/9x10

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5+...-1/10

=1-1/10

=9/10

ta có :(1/1-1/6).10-x=0

=>5/6.10-x=0

    25/3-x=0

=>x=25/3

1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6

Đặt A = 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6

A = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6

A = 1/1 - 1/6

A = 5/6

Vậy A = 5/6

C=2+3/2+4/3+5/4+6/5

C=437/60

\(C=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}\)

\(C=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(C=1-\frac{1}{6}\)

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

1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7

=1/1-1/2+1/2-1/3+...-1/7

=1+(1/2-1/2+1/3-1/3+...+1/6-1/6)-1/7

=1 +0+0+...-1/7

=1-1/7

=6/7

hình như là 8/7
 

Kếết quả là 116/24

Rút gọn ra phân số tối giản là 29/6

=1x2x3+2x3x3+...+98x99x3

=1x2x3+2x3x(4-1)+...+98x99x(100-97)

=1x2x3+2x3x4-1x2x3+...+98x99x100-97x98x99

=98x99x100

=970200

1> a) \(\frac{5}{7}x4:\frac{5}{9}=\frac{5}{7}:\frac{5}{9}x4=\frac{5}{7}x\frac{9}{5}x4=\frac{9}{7}x4=\frac{9x4}{7}=\frac{36}{7}\)

\(b,8x\frac{2}{3}:\frac{1}{2}=8x\frac{2}{3}x\frac{2}{1}=8x2x\frac{2}{3}=16x\frac{2}{3}=\frac{32}{3}\)

\(c,6:\frac{3}{5}-\frac{7}{6}x\frac{6}{7}=6x\frac{5}{3}-1=10-1=9\)

\(\frac{21}{5}x\frac{10}{11}+\frac{57}{11}=\frac{42}{11}+\frac{57}{11}=\frac{99}{11}=9\)

2) a) \(\frac{35}{9}:x=\frac{35}{6}\)

\(x=\frac{35}{9}:\frac{35}{6}\)

\(x=\frac{35}{9}x\frac{6}{35}\)

\(x=\frac{2}{3}\)

b) \(\left(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}\right)x10-X=0\)

\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{5}-\frac{1}{6}\right)x10-X=0\)

\(\left(\frac{1}{1}-\frac{1}{6}\right)x10-X=10\)

\(\frac{5}{6}x10-X=0\)

\(X=\frac{5}{6}x10=\frac{25}{3}\)

Đúng nha !!!!

1/a/\(\frac{5}{7}\cdot4:\frac{5}{9}=\frac{20}{7}:\frac{5}{9}=\frac{20}{7}\cdot\frac{9}{5}=\frac{36}{7}\)

b/\(8\cdot\frac{2}{3}:\frac{1}{2}=\frac{16}{3}:\frac{1}{2}=\frac{16}{3}\cdot\frac{2}{1}=\frac{32}{3}\)

c/\(6:\frac{3}{5}-\frac{7}{6}\cdot\frac{6}{7}=6\cdot\frac{5}{3}-1=10-1=9\)

2/a/\(\frac{35}{9}:x=\frac{35}{6}\)

\(x=\frac{35}{9}:\frac{35}{6}=\frac{35}{9}\cdot\frac{6}{35}\)

\(x=\frac{2}{3}\)

b/\(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\right)\cdot10-x=0\)

\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\cdot10-x=0\)

\(\left(\frac{30}{60}+\frac{10}{60}+\frac{5}{60}+\frac{2}{30}\right)\cdot10-x=0\)

\(\frac{47}{60}\cdot10-x=0\)

\(\frac{47}{6}-x=0\)

\(x=\frac{47}{6}-0\)

\(x=\frac{47}{6}\)

xs

đặt A=1/1x2+1/2x3+1/3x4+1/4x5+1/5x6

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{5}-\frac{1}{6}\)

\(=1-\frac{1}{6}\)

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

nhanh lên mọi người ơi , mình đang vội☹

1/1x2 + 1/2x3 + 1/3x4 +1/4x5 +1/5x6

= 1 -1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6

= 1 - 1/6 = 5/6

`x/(x+1)=1/(1xx2)+1/(2xx3)+1/(3xx4)+...+1/(31xx32)`

`=>x/(x+1)=1-1/2+1/2-1/3+1/3-1/4+...+1/31-1/32`

`=>x/(x+1)=1-1/32`

`=>x/(x+1)=31/32`

`=>32x=31(x+1)`

`=>32x=31x+31`

`=>32x-31x=31`

`=>x=31`

31/31