N=7/2(2/1.3+....+2/13.15)

N=7/2.(1/1-1/3+.....+1/13-1/15)

N=7/2.(1-1/15)

N=7/2.(14/15)

N=7.14/2.15

Bạn giải M luôn dc ko?

Dễ lắm bạn.Suy nghĩ 1 tí là ra

\(\dfrac{7}{19}x\dfrac{8}{23}+\dfrac{7}{19}x\dfrac{15}{23}+1\dfrac{7}{19}\)

= \(\dfrac{7}{19}x\left(\dfrac{8}{23}+\dfrac{15}{23}\right)+1+\dfrac{7}{19}\)

=\(\dfrac{7}{19}x1+1+\dfrac{7}{19}\)

= \(\dfrac{7}{19}+1+\dfrac{7}{19}=1\dfrac{14}{19}\) = \(\dfrac{33}{19}\)

\(\dfrac{75}{100}+\dfrac{18}{21}+\dfrac{49}{32}+\dfrac{1}{4}+\dfrac{3}{21}-\dfrac{17}{32}\)

=  \(\dfrac{3}{4}+\dfrac{6}{7}+\dfrac{49}{32}+\dfrac{1}{4}+\dfrac{1}{7}-\dfrac{17}{32}\)

= \(\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+\left(\dfrac{6}{7}+\dfrac{1}{7}\right)+\left(\dfrac{49}{32}-\dfrac{17}{32}\right)\)

= 1 + 1 + 1 = 3

\(\dfrac{8}{9}x\dfrac{15}{16}x\dfrac{24}{25}x\dfrac{35}{36}x\dfrac{48}{49}x\dfrac{63}{64}\)

= \(\dfrac{3}{4}\) *Câu này bạn tự sử dụng gạch nhé!

`1,`

`a,`

`7/19 \times 8/23 + 7/19 \times 15/23 + 1 7/19`

`= 7/19 \times 8/23 + 7/19 \times 15/23 + 1 + 7/19`

`= 7/19 \times (8/23 + 15/23 + 1) + 1`

`= 7/19 \times 2 + 1`

`=14/19 + 1`

`= 33/19`

`b,`

`75/100 + 18/21 + 49/32 + 1/4 + 3/21 - 17/32`

`= 75/100 + (18/21 + 3/21) + (49/32 - 17/32) + 1/4`

`= 0,75 + 1 + 1 + 0,25`

`= (0,75 + 0,25) + 1 + 1`

`= 1+1+1=3`

`c,`

`8/9 \times 15/16 \times 24/25 \times 35/36 \times 48/49 \times 63/64`

`=` \(\dfrac{2\times3}{3\times3}\times\dfrac{3\times5}{4\times4}\times\dfrac{3\times4\times2}{5\times5}\times\dfrac{5\times7}{6\times6}\times\dfrac{6\times8}{7\times7}\times\dfrac{7\times9}{8\times8}\)

`= 3/4` (bạn sử dụng gạch, rút gọn các số là được nhé).

\(2B=\frac{2}{1.3}+\frac{2}{3.5}+....+\frac{2}{9.11}\)

\(2B=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\)

\(2B=\frac{1}{1}-\frac{1}{11}=\frac{10}{11}\)

\(B=\frac{10}{11}:2=\frac{10}{11}.\frac{1}{2}=\frac{5}{11}\)

\(B=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{7.9}+\frac{2}{9.11}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{1}{2}.\frac{10}{11}=\frac{5}{11}\)

B = 1/3 + 1/15 + 1/35 + 1/63 + 1/99

B = 1/2 × (2/1×3 + 2/3×5 + 2/5×7 + 2/7×9 + 2/9×11)

B = 1/2 × (1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11)

B = 1/2 × (1 - 1/11)

B = 1/2 × 10/11

B = 5/11

\(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{25}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)

\(=\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+\dfrac{2}{9\cdot11}+\dfrac{2}{11\cdot13}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-...+\dfrac{1}{11}-\dfrac{1}{13}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\left(1-\dfrac{1}{3}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\dfrac{2}{3}\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\dfrac{1}{3}+\dfrac{1}{25}\)

\(=\dfrac{28}{75}\)

cám ơi bạn

cảm ơn bạn rất nhiều

P=1/3+1/15+1/35+1/63+1/99
  =1:3+1:15+1:35+1:63+1:99
  =1:(3+15+35+63+99)
  =1:215
  =1/215
Vậy:P=1/215

a) CÓ: A = (1-1/4²).(1-1/5²).(1-1/6²)......(1-1/200²)

               =\(\frac{4^2-1^2}{4^2}\). \(\frac{5^2-1^2}{5^2}\). \(\frac{6^2-1^2}{6^2}\)....... \(\frac{200^2-1^2}{200^2}\)

Ta có công thức sau : a²-b²= a² -ab+ab-b² 

                                            = a(a-b) + b(a-b)

                                            = (a+b)(a-b)

   ÁP DỤNG CÔNG THỨC TRÊN VÀO BÀI TOÁN TA ĐƯỢC : 

  A=  \(\frac{3.5}{4^2}\). \(\frac{4.6}{5^2}\). \(\frac{5.7}{6^2}\)......\(\frac{199.201}{200^2}\)

    = \(\frac{\left(3.4.5.....199\right)\left(5.6.7....201\right)}{\left(4.5.6......200\right)^2}\)

    =    \(\frac{\left(3.4.5.......199\right)\left(5.6.7.....200.201\right)}{\left(4.5.6.....199.200\right)\left(4.5.6......200\right)}\)

    =   \(\frac{3.201}{200.4}\)

   =  \(\frac{603}{800}\)​​

b)Từ đề bài ta suy ra : B=\(\frac{1.3}{5.7}\).\(\frac{3.5}{7.9}\). \(\frac{5.7}{9.11}\)...... \(\frac{99.101}{103.105}\)

                                      = \(\frac{1.3^2.5^2.7^2......99^2.101}{5.7^2.9^2.11^2....99^2.101^2.103^2.105}\)

                                      =\(\frac{3^2.5}{101.103^2.105}\)

                                       =\(\frac{3}{7500563}\)

\(A=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+...+\frac{1}{9999}\)

   \(=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{99.101}\)

   \(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}\right)+\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}\right)+\frac{1}{2}.\left(\frac{1}{7}-\frac{1}{9}\right)+...+\frac{1}{2}\left(\frac{1}{99}-\frac{1}{101}\right)\)

   \(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\right)\)

   \(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{101}\right)\)

   \(=\frac{1}{2}.\frac{98}{303}\)

   \(=\frac{49}{303}\)

Dấu chấm(.) ở cấp hai là dấu nhân (x)

tk đi rồi mk tk lại......

A=1/3.5+1/5.7+1/7.9+1/9.11+1/11.13

A=1/2 [1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13]

A=1/2.10/39

A=5/39

ai tk mình

mình tk lại

=5/39

 tk mk đi mk tk cho hứa đó

\(a)\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{132}\)

\(=\frac{22}{132}+\frac{11}{132}+\frac{1}{20}+\frac{1}{132}\)

\(=\frac{33}{132}+\frac{1}{20}+\frac{1}{132}\)

\(=\frac{34}{132}+\frac{1}{20}\)

\(=\frac{17}{66}+\frac{1}{20}\)

\(=\frac{203}{660}\)

\(a,\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{132}\) 

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{132}\)

\(=\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\right)+\frac{1}{132}\)

\(=\left(\frac{1}{2}-\frac{1}{5}\right)+\frac{1}{132}\)

\(=\frac{3}{10}+\frac{1}{132}\)

\(=\frac{198}{660}+\frac{5}{660}\)

\(=\frac{203}{660}\)

1/6 + 1/12 + 1/20 + ... + 1/132

= 1/2x3 + 1/3x4 + 1/3x4 + 1/4x5 + ... + 1/11x12

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + .... + 1/11 + 1/12

= 1/2 - 1/12

= 5/12

Bài  2 

= 1/3x5 + 1/5x7 + 1/7x9 + 1/9x11 + 1/11x13

= 1/2 x ( 2/3x5 + 2/5x7 + 2/7x9 + 2/9x11 + 2/11x13

= 1/2 x ( 2/3 - 2/5 + 2/5 - 2/7 + 2/7 - 2/9 + 2/9 - 2/11 + 2/11 - 2/13

= 1/2 x ( 2/3 - 2/13 )

= 1/2 x 20/39

= 10 / 39