`11/(5.7) + 11/(7.9) + 11/(9.11) + ... + 11/(59.61)`

`= 2.(11/(5.7) + 11/(7.9) + ... + 11/(59.61))`

`= 11.(2/(5.7) + 2/(7.9) + ... + 2/(59.61))`

`= 11.(1/5 - 1/7 + 1/7 - 1/9 + ... +1/59 - 1/61)`

`= 11.(1/5 - 1/61)`

`= 11.56/305`

`= 616/305`

`11/(5.7) + 11/(7.9) + 11/(9.11) + ... + 11/(59.61)`

`= 2.(11/(5.7) + 11/(7.9) + ... + 11/(59.61))`

`= 11.(2/(5.7) + 2/(7.9) + ... + 2/(59.61))`

`= 11.(1/5 - 1/7 + 1/7 - 1/9 + ... +1/59 - 1/61)`

`= 11.(1/5 - 1/61)`

`= 11.56/305`

`= 616/305`

`= 616/305 : 2`

`= 308/305`

E = \(\frac{11}{5.7}+\frac{11}{7.9}+...+\frac{11}{59.61}=11.\frac{1}{2}\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)

E = \(\frac{11}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)

E = \(\frac{11}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)=\frac{11}{2}.\frac{56}{305}\)

E = \(\frac{308}{305}\)

E = 11/2 ( 2/5.7 + ... +2/59.61)

   = 11/2 ( 1/5 - 1/7 + 1/7 - 1/9 + ... + 1/59 - 1/61)

   = 11/2 ( 1/5 - 1/61)

= 11/2 .56/305

 =308/305

\(E=\frac{11}{5.7}+\frac{11}{7.9}+.....+\frac{11}{59,61}\)

\(E=\frac{11}{2}\left(\frac{1}{5}-\frac{1}{7}+....+\frac{1}{59}-\frac{1}{61}\right)\)

\(E=\frac{11}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)\)

\(E=\frac{11}{2}.\frac{56}{305}=\frac{308}{305}\)

a,Ta có : \(\frac{1}{a}+\frac{-1}{a+1}=\frac{1}{a}-\frac{1}{a+1}\)

=\(\frac{a+1-a}{a\left(a+1\right)}=\frac{1}{a\left(a+1\right)}\)(Đpcm)

b,\(\frac{11}{5.7}+\frac{11}{7.9}+\frac{11}{9.11}+.....+\frac{11}{59.61}\)

=\(\frac{11}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+.....+\frac{2}{59.61}\right)\)

=\(\frac{11}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+......+\frac{1}{59}-\frac{1}{61}\right)\)

=\(\frac{11}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)=\frac{308}{305}\)

=> \(\Rightarrow\left(\frac{11}{5}-\frac{11}{7}+\frac{11}{7}-\frac{11}{9}+...+\frac{11}{59}-\frac{11}{61}\right):2=\left(\frac{11}{5}-\frac{11}{61}\right):2=\frac{616}{305}:2=\frac{308}{305}\)

Đặt \(A=\frac{11}{5.7}+\frac{11}{7.9}+...+\frac{11}{59.61}\)

\(\Rightarrow2A:11=\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\)

\(\Rightarrow2A:11=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\)

\(\Rightarrow2A:11=\frac{1}{5}-\frac{1}{61}\)

\(\Rightarrow2A:11=\frac{56}{305}\)

\(\Rightarrow2A=\frac{56}{305}.11=\frac{616}{305}\)

\(\Rightarrow A=\frac{616}{305}:2=\frac{308}{305}\)

Vậy kết quả của phép tính trên là \(\frac{308}{305}\)

11/2x(1/5-1/7+1/7+1/9+.....+1/59-1/61)

=11/2x(1/5-1/61)

=11/2x56/305

=308/305

Bạn gõ thiều phân số \(\frac{1}{3.5}\)à?

1)

2/3.5+2/5.7+...+2/11.13+2/13.15+2/1.2+2/2.3+...+2/9.10

=(2/3.5+...2/13.15)+(2/1.2+...+2/9.10)

= (2/3-2/15)+ [2(1-1/10)]

=8/15+9/5

=7/3

2)

11/12+11/12.24+...+11/88.99

=11-1/9

=10/8/9

Mik giải phía dưới rồi đó. Câu lúc nãy bạn đăng ý

\(\left[\frac{12}{11}-\left(\frac{1}{2}+\frac{1}{44}\right)\right].\left(x-0,2\right)=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)

\(\frac{25}{44}.\left(x-0,2\right)=\frac{1}{2}.\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{9.11}\right)\)

\(x-0,2=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\right):\frac{25}{44}\)

\(x-\frac{1}{5}=\frac{22}{25}.\left(1-\frac{1}{11}\right)=\frac{22}{25}.\frac{10}{11}=\frac{4}{5}\)

\(x=\frac{4}{5}+\frac{1}{5}\)

\(x=1\)

84/305 nha bạn

mk nha có cần giải ra ko