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Đặt \(A=\frac{9+\frac{9}{11}+\frac{18}{23}-\frac{27}{37}}{8+\frac{8}{11}+\frac{16}{23}-\frac{24}{37}}-\frac{2+\frac{16}{29}-\frac{24}{13}-\frac{32}{11}}{3+\frac{24}{29}-\frac{36}{13}-\frac{48}{11}}\)\(=\frac{9\left(1+\frac{1}{11}+\frac{2}{23}-\frac{3}{37}\right)}{8\left(1+\frac{1}{11}+\frac{2}{23}-\frac{3}{37}\right)}-\frac{2\left(1+\frac{8}{29}-\frac{12}{13}-\frac{16}{11}\right)}{3\left(1+\frac{8}{29}-\frac{12}{13}-\frac{16}{11}\right)}\)
\(=\frac{9}{8}-\frac{2}{3}\)(do \(1+\frac{1}{11}+\frac{2}{23}-\frac{3}{37};1+\frac{8}{29}-\frac{12}{13}-\frac{16}{11}\ne0\))
\(=\frac{27}{24}-\frac{16}{24}=\frac{11}{24}.\)
Vậy A = \(\frac{11}{24}.\)
= 2/2 . ( 4 / 5.7 +4 / 7.9 +...+ 4 / 59.61 )
= 4/2 . ( 2 / 5.7 +2 / 7.9 +...+ 2 / 59.61 )
= 2 . ( 7-5 / 5.7 + 9-7 / 7.9 +...+ 61-59 / 59.61 )
= 2 . ( 1/5 - 1/7 + 1/7 - 1/9 +...+ 1/59 - 1/61 )
= 2 . ( 1/5 - 1/61 )
= 2 . ( 61/305 - 5/305 )
= 2 . 56/305
= 112/305
ảnh anime đẹp thế là anime gì vậy bạn
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,\(\frac{11}{5.7}+\frac{11}{7.9}+\frac{11}{9.11}+.....+\frac{11}{59.61}\)
=\(\frac{11}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+.....+\frac{2}{59.61}\right)\)
=\(\frac{11}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+......+\frac{1}{59}-\frac{1}{61}\right)\)
=\(\frac{11}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)=\frac{308}{305}\)
mình ko ghi lại đề nha!
ta có
1/1-1/2+1/2-1/3+...............+1/999-1/1000
=1/1-1/1000
=999/1000
ta co;1-1/2+1/2-1/3+...+1/999-1/1000
=1+(-1/2+1/2)+...+(1/999-1/999)-1/100
=1-1/1000=999/1000
MK NHA BN
a,Gọi tổng trên là A.
Xét \(\frac{4}{5}-\frac{4}{7}=\frac{8}{35};...;\frac{4}{59}-\frac{4}{61}=\frac{8}{3599}\)=>\(A=\frac{1}{2}.\left(\frac{4}{5}-\frac{4}{7}+\frac{4}{7}-\frac{4}{9}+...+\frac{4}{59}-\frac{4}{61}\right)\)\(=\frac{1}{2}.\left(\frac{4}{5}-\frac{4}{61}\right)=\frac{1}{2}.\frac{224}{305}=\frac{112}{305}\)
b,Gọi tổng trên là B
Theo đề bài ta có:\(B=\frac{24.47-23}{24+47.23}.\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}-\frac{9}{11}+9}\)=\(\frac{\left(23+1\right).47-23}{24+47.23}.\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}-\frac{9}{11}+9}=\frac{47.23+24}{24+47.23}.\frac{3.\left(1+\frac{1}{7}-\frac{1}{11}+\frac{1}{1001}-\frac{1}{13}\right)}{3.\left(3+\frac{3}{1001}-\frac{3}{13}+\frac{3}{7}-\frac{3}{11}\right)}\)\(=\frac{1+\frac{1}{1001}-\frac{1}{13}+\frac{1}{7}-\frac{1}{11}}{3+\frac{3}{1001}-\frac{3}{13}+\frac{3}{7}-\frac{3}{11}}=\frac{1+\frac{1}{1001}-\frac{1}{13}+\frac{1}{7}-\frac{1}{11}}{3.\left(1+\frac{1}{1001}-\frac{1}{13}+\frac{1}{7}-\frac{1}{11}\right)}=\frac{1}{3}\)
\(2\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)
\(=2\left(\frac{1}{5}-\frac{1}{61}\right)=2\left(\frac{61-5}{305}\right)=2.\frac{56}{305}=\frac{112}{305}\)
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
Em nhớ nhân 1/2 trong tất cả dấu bằng thì biểu thức này mới không thay đổi kết quả nhé.
`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`
=> \(\Rightarrow\left(\frac{11}{5}-\frac{11}{7}+\frac{11}{7}-\frac{11}{9}+...+\frac{11}{59}-\frac{11}{61}\right):2=\left(\frac{11}{5}-\frac{11}{61}\right):2=\frac{616}{305}:2=\frac{308}{305}\)
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 \(\frac{308}{305}\)