Ta có: \(\frac{1}{\left(2n+1\right)\left(2n+3\right)}-\frac{1}{\left(2n+3\right)\left(2n+5\right)}\)

\(=\frac{2n+5-\left(2n+1\right)}{\left(2n+1\right)\left(2n+3\right)\left(2n+5\right)}\)

\(=\frac{4}{\left(2n+1\right)\left(2n+3\right)\left(2n+5\right)}\)

=>\(\frac{1}{\left(2n+1\right)\left(2n+3\right)\left(2n+5\right)}=\frac14\left(\frac{1}{\left(2n+1\right)\left(2n+3\right)}-\frac{1}{\left(2n+3\right)\left(2n+5\right)}\right)\)

Do đó, ta có:

\(\frac{1}{1\cdot3\cdot5}=\frac14\left(\frac{1}{1\cdot3}-\frac{1}{3\cdot5}\right)\)

\(\frac{1}{3\cdot5\cdot7}=\frac14\left(\frac{1}{3\cdot5}-\frac{1}{5\cdot7}\right)\)

...

\(\frac{1}{25\cdot27\cdot29}=\frac14\left(\frac{1}{25\cdot27}-\frac{1}{27\cdot29}\right)\)

Do đó: \(\frac{1}{1\cdot3\cdot5}+\frac{1}{3\cdot5\cdot7}+\cdots+\frac{1}{25\cdot27\cdot29}=\frac14\left(\frac{1}{1\cdot3}-\frac{1}{3\cdot5}+\frac{1}{3\cdot5}-\frac{1}{5\cdot7}+\cdots+\frac{1}{25\cdot27}-\frac{1}{27\cdot29}\right)\)

\(=\frac14\left(\frac{1}{1\cdot3}-\frac{1}{27\cdot29}\right)\)

=>\(36\left(\frac{1}{1\cdot3\cdot5}+\frac{1}{3\cdot5\cdot7}+\cdots+\frac{1}{25\cdot27\cdot29}\right)=36\cdot\frac14\left(\frac{1}{1\cdot3}-\frac{1}{27\cdot29}\right)\)

=>\(\frac{36}{1\cdot3\cdot5}+\frac{36}{3\cdot5\cdot7}+\cdots+\frac{36}{25\cdot27\cdot29}=9\left(\frac13-\frac{1}{27\cdot29}\right)=3-\frac{1}{3\cdot29}=\frac{3\cdot3\cdot29-1}{3\cdot29}=\frac{260}{87}\)

bang 0

Bạn cho mình đề bài

đúng rồi

7 x 8 = 56       16 : 2 = 8       36 : 6 = 6       49 : 7 = 7

2 x 5 = 10       72 : 8 = 9       9 x 3 = 27       63 : 7 = 9

6 x 4 = 24       25 : 5 = 5       4 x 8 = 32       7 x 5 = 35

7 x 8 = 56

2 x 5 = 10

6 x 4 = 24

16 : 2 = 8 

72 : 8 = 9

25 : 5 = 5

36 : 6 = 6

9 x 3 = 27

4 x 8 = 32

49 : 7 = 7

63 : 7 = 9

7 x 5 = 35

\(a)\dfrac{3}{4}-\dfrac{2}{7}=\dfrac{21-8}{28}=\dfrac{13}{28}.\\ b)\dfrac{3}{8}-\dfrac{5}{16}=\dfrac{6-5}{16}=\dfrac{1}{16}.\)

\(c)\dfrac{7}{5}-\dfrac{2}{3}=\dfrac{21-10}{15}=\dfrac{11}{15}.\\ d)\dfrac{31}{36}-\dfrac{5}{6}=\dfrac{31-30}{36}=\dfrac{1}{36}.\)

Bài 2. > , < ,  = ?

5/7 < 4/3             2/5 < 6/10            1/4 = 3/12                27/36 >

2/9           7/6 > 7/9

7/2 = 2/7        15/23 < 1                  27/9 > 2          14/15 < 1          51/17 < 4

a: x/147=5/7

=>x=147*5/7=105

b: x-2/36=7/12

=>x-2/36=21/36

=>x=21/36+2/36=23/36

Cách 1

\(2\dfrac{3}{4}\)+ \(5\dfrac{7}{9}\)= \(\dfrac{11}{4}+\dfrac{47}{9}\)

= \(\dfrac{99}{36}+\dfrac{188}{36}\)

= \(\dfrac{287}{36}\)= 7,9722...

Cách 2

\(2\dfrac{3}{4}+5\dfrac{7}{8}=2\dfrac{55}{36}+5\dfrac{55}{36}\)

= \(7\dfrac{55}{36}=8\dfrac{19}{36}\)

Cách 1 mình làm nhầm bài đúng phải là

\(2\dfrac{3}{4}+5\dfrac{7}{9}=\dfrac{11}{4}+\dfrac{52}{9}=\dfrac{99}{36}+\dfrac{208}{36}\)

=\(\dfrac{307}{36}\)=8,527777778