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HT
9 tháng 8 2015
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 = \(\frac{308}{305}\)
9 tháng 8 2015
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
24 tháng 6 2019
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,\(\frac{11}{5.7}+\frac{11}{7.9}+\frac{11}{9.11}+.....+\frac{11}{59.61}\)
=\(\frac{11}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+.....+\frac{2}{59.61}\right)\)
=\(\frac{11}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+......+\frac{1}{59}-\frac{1}{61}\right)\)
=\(\frac{11}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)=\frac{308}{305}\)
MC
12 tháng 3 2016
=> \(\Rightarrow\left(\frac{11}{5}-\frac{11}{7}+\frac{11}{7}-\frac{11}{9}+...+\frac{11}{59}-\frac{11}{61}\right):2=\left(\frac{11}{5}-\frac{11}{61}\right):2=\frac{616}{305}:2=\frac{308}{305}\)
12 tháng 3 2016
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 \(\frac{308}{305}\)
CM
3
27 tháng 3 2016
Đặt 2/5 ra ngoài rồi tách từng cặp phân số ra sau đó bn tự làm nhé!
27 tháng 3 2016
A=\(\frac{5}{5.7}+\frac{5}{7.9}+.........+\frac{5}{59.61}\)
=\(\frac{5}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+.........+\frac{2}{59.61}\right)\)
=\(\frac{5}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...........+\frac{1}{59}-\frac{1}{61}\right)\)
=\(\frac{5}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)\)
=\(\frac{5}{2}.\frac{56}{305}\)
=\(\frac{28}{61}\)
15 tháng 3 2018
\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{9\cdot11}\)
\(=\frac{1}{2}\cdot\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{9\cdot11}\right)\)
\(=\frac{1}{2}\left(\frac{3-1}{1\cdot3}+\frac{5-3}{3\cdot5}+\frac{7-5}{5\cdot7}+...+\frac{11-9}{9\cdot11}\right)\)
\(=\frac{1}{2}\left(\frac{3}{1\cdot3}-\frac{1}{1\cdot3}+\frac{5}{3\cdot5}-\frac{3}{3\cdot5}+...+\frac{7}{5\cdot7}-\frac{5}{5\cdot7}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{11}\right)\)
\(=\frac{1}{2}\cdot\frac{10}{11}\)
\(=\frac{10}{22}=\frac{5}{11}\)
15 tháng 3 2018
Ta có :
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
\(=\)\(\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\)\(\frac{1}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\)\(\frac{1}{2}\left(1-\frac{1}{11}\right)\)
\(=\)\(\frac{1}{2}.\frac{10}{11}\)
\(=\)\(\frac{5}{11}\)
Bạn làm đúng òi
Chúc bạn học tốt ~
3 tháng 4 2019
2\3x-780\11:[13\2.(1\3.5+1\5.7+1\7.9+1\9.11]=-5
2\3x-780\11:[13\2.(1\3-1\5+1\5-1\7+....+1\9-1\11)]=-5
2\3x-780\11:[13\2.(1\3-1\11)]=-5
2\3x-780\11:[13\2.8\33]=-5
2\3x-780\11:52\33=-5
2\3x-525\13=-5
2\3x=-5+525\13
2\3x=460\13
x=460\13:2\3
x=690\13
NN
4
14 tháng 3 2017
\(T=\dfrac{3}{5\cdot7}+\dfrac{3}{7\cdot9}+\dfrac{3}{9\cdot11}+...+\dfrac{3}{59\cdot61}\)
\(=\dfrac{3}{2}\cdot\left(\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+\dfrac{2}{9\cdot11}+...+\dfrac{2}{59\cdot61}\right)\)
\(=\dfrac{3}{2}\cdot\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{59}-\dfrac{1}{61}\right)\)
\(=\dfrac{3}{2}\cdot\left(\dfrac{1}{5}-\dfrac{1}{61}\right)=\dfrac{3}{2}\cdot\dfrac{56}{305}=\dfrac{84}{305}\)
14 tháng 3 2017
\(\dfrac{3}{5.7}+\dfrac{3}{7.9}+\dfrac{3}{9.11}+...+\dfrac{3}{59.61}\)
\(=3.\left(\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+...+\dfrac{1}{59.61}\right)\)
\(=3.\dfrac{1}{2}.\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+....+\dfrac{1}{59}-\dfrac{1}{61}\right)\)
\(=\dfrac{3}{2}.\left(\dfrac{1}{5}-\dfrac{1}{61}\right)\)
\(=\dfrac{3}{2}.\dfrac{56}{305}\)
\(=\dfrac{84}{305}\)
