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

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}=\)

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

\(\frac{1}{1}-\frac{1}{6}=\frac{5}{6}\)

k nha gõ mỏi tay lắm

149/240

nguyễn trần đức kông bn phải giải rõ ràng ra chứ, 

a.\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2015}\right)=\frac{1}{2}.\frac{2}{3}...\frac{2014}{2015}=\frac{1.2.3...2014}{2.3...2015}=\frac{1}{2015}\)

b.\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{128}-\frac{1}{256}=1-\frac{1}{256}=\frac{255}{256}\)

c.\(\frac{5}{2}+\frac{5}{4}+\frac{5}{8}+...+\frac{5}{256}=5\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\right)=5.\frac{255}{256}=\frac{1275}{256}\)

d.14,35+(13,7-13,6).1=14,35+0,1.1=14,35+0,1=14,45

a.1/2015

Bài 1

a) 3 2/5 - 1/2

= 17/5 - 1/2

= 34/10 - 5/10

= 29/10

b) 4/5 + 1/5 × 3/4

= 4/5 + 3/20

= 16/20 + 3/20

= 19/20

c) 3 1/2 × 1 1/7

= 7/2 × 8/7

= 4

d) 4 1/6 : 2 1/3

= 25/6 : 7/3

= 25/14

Bài 2

a) 3 × 1/2 + 1/4 × 1/3

= 3/2 + 1/12

= 18/12 + 1/12

= 19/12

b) 1 4/5 - 2/3 : 2 1/3

= 9/5 - 2/3 : 7/3

= 9/5 - 2/7

= 63/35 - 10/35

= 53/35

Bài 1

a) 3 2/5 - 1/2

= 17/5 - 1/2

= 34/10 - 5/10

= 29/10

b) 4/5 + 1/5 × 3/4

= 4/5 + 3/20

= 16/20 + 3/20

= 19/20

c) 3 1/2 × 1 1/7

= 7/2 × 8/7

= 4

d) 4 1/6 : 2 1/3

= 25/6 : 7/3

= 25/14

bủh

\(...=\dfrac{3}{2}x\dfrac{4}{3}x\dfrac{5}{4}x\dfrac{6}{5}x\dfrac{7}{6}....x\dfrac{1000}{999}\)

\(=\dfrac{1}{2}x\dfrac{1000}{1}=500\)

=3/2x4/3x5/4x....x1000/999

=1/2x1000=500

mình chưa chắc là đúng đâu nhé

Giải đấy đủ giúp mình với 

a: =8/15x1/4=2/15

b: \(=\dfrac{5}{3}\cdot\dfrac{4}{5}\cdot\dfrac{6}{7}=\dfrac{24}{21}=\dfrac{8}{7}\)

c: \(=\dfrac{2}{5}\left(\dfrac{3}{7}+\dfrac{4}{7}\right)=\dfrac{2}{5}\)

a: \(=\dfrac{2}{3}\cdot\dfrac{4}{5}\cdot\dfrac{5}{6}=\dfrac{2}{3}\cdot\dfrac{2}{3}=\dfrac{4}{9}\)

b: \(=\dfrac{5}{6}\cdot\dfrac{1}{5}=\dfrac{1}{6}\)

a. C1: \(\dfrac{8}{15}.\dfrac{5}{6}=\dfrac{4}{9}\)

C2: \(\dfrac{2}{3}.\dfrac{4}{5}.\dfrac{5}{6}=\dfrac{2.4.5}{3.5.3.2}\)

Triệt tiêu phần giống nhau ở tử và mẫu ta có 

\(=\dfrac{4}{9}\)

b. \(C1:\left(\dfrac{1}{2}+\dfrac{1}{3}\right).\dfrac{1}{5}=\dfrac{5}{6}.\dfrac{1}{5}=\dfrac{1}{6}\)

C2: \(\dfrac{1}{2}.\dfrac{1}{5}+\dfrac{1}{3}.\dfrac{1}{5}=\dfrac{1}{10}+\dfrac{1}{15}=\dfrac{1}{6}\)

Cách 1:

$(\frac{2}{3}\times \frac{4}{5})\times \frac{5}{6}=\frac{8}{15}\times \frac{5}{6}=\frac{8\times 5}{15\times 6}=\frac{2\times 2\times 2\times 5}{3\times 5\times 2\times 3}=\frac{4}{9}$

Cách 2:

$(\frac{2}{3}\times \frac{4}{5})\times \frac{5}{6}=\frac{2}{3}\times (\frac{4}{5}\times \frac{5}{6})=\frac{2}{3}\times \frac{4}{6}=\frac{2\times 4}{3\times 6}=\frac{2\times 4}{3\times 2\times 3}=\frac{4}{9}$

Cách 1:

$(\frac{1}{2}+\frac{1}{3})\times \frac{1}{5}=\left(\frac{3+2}{6}\right)\times \frac{1}{5}=\frac{5}{6}\times \frac{1}{5}=\frac{1}{6}$

Cách 2:

$(\frac{1}{2}+\frac{1}{3})\times \frac{1}{5}=\frac{1}{2}\times \frac{1}{5}+\frac{1}{3}\times \frac{1}{5}=\frac{1}{10}+\frac{1}{15}=\frac{3}{30}+\frac{2}{30}=\frac{5}{30}=\frac{1}{6}$

Bài 1:

câu a: 4\(\dfrac{4}{9}\) : 2\(\dfrac{2}{3}\) + 3\(\dfrac{1}{6}\)

        = \(\dfrac{40}{9}\) : \(\dfrac{8}{3}\) + \(\dfrac{19}{6}\)

        = \(\dfrac{5}{3}\) + \(\dfrac{19}{6}\)

         = \(\dfrac{10}{6}\) + \(\dfrac{19}{6}\)

          = \(\dfrac{29}{6}\)

b, (15,25 + 3,75) \(\times\) 4 + ( 20,71 + 5,29)\(\times\) 5

     = 19 \(\times\) 4 + 26 \(\times\) 5

     = 76 + 130

     = 206

c, \(\dfrac{4}{5}\) \(\times\) \(\dfrac{1}{2}\) + \(\dfrac{4}{5}\) \(\times\) \(\dfrac{1}{3}\) - \(\dfrac{4}{5}\) \(\times\) \(\dfrac{1}{4}\)

= \(\dfrac{2}{5}\)    + \(\dfrac{4}{15}\) - \(\dfrac{1}{5}\)

= \(\dfrac{6}{15}\) + \(\dfrac{4}{15}\) - \(\dfrac{3}{15}\)

= \(\dfrac{7}{15}\) 

d, 1\(\dfrac{5}{7}\) + 7\(\dfrac{3}{6}\) + 2\(\dfrac{2}{7}\) - 4\(\dfrac{3}{6}\)

= (1 + 2 + \(\dfrac{5}{7}\) + \(\dfrac{2}{7}\)) + ( 7 + \(\dfrac{3}{6}\) - 4 - \(\dfrac{3}{6}\))

=  3 + 1 + 3 

= 7

e, 8,4 \(\times\) \(x\) + 1,6 \(\times\) \(x\) = 10

   (8,4 + 1,6) \(\times\) \(x\)      = 10

     10 \(\times\) \(x\)                = 10

               \(x\)                = 1