CM
3
K
Khách
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22 tháng 2 2023
1: \(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{11}-\dfrac{1}{13}\right)\)
=1/2*10/39
=5/39
2: \(=\dfrac{5}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{11}\right)=\dfrac{5}{2}\cdot\dfrac{10}{11}=\dfrac{50}{22}=\dfrac{25}{11}\)
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
\(\dfrac{3}{5.7}+\dfrac{3}{7.9}+\dfrac{3}{9.11}+...+\dfrac{3}{59.61}\)
\(=3.\left(\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+...+\dfrac{1}{59.61}\right)\)
\(=3.\dfrac{1}{2}.\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+....+\dfrac{1}{59}-\dfrac{1}{61}\right)\)
\(=\dfrac{3}{2}.\left(\dfrac{1}{5}-\dfrac{1}{61}\right)\)
\(=\dfrac{3}{2}.\dfrac{56}{305}\)
\(=\dfrac{84}{305}\)
18 tháng 5 2018
1) P = 2/3.5 + 2/5.7 + 2/7.9 + 2/9.11 + 2/11.13 + 2/13.15
P= (1/3-1/5) + (1/5-1/7) + (1/7-1/9) + (1/9-1/11) + (1/11-1/13) + (1/13-1/15)
P=1/3-1/15= 4/15
2) a/ 0,2:1+3/5+80%
= 2/10:8/5+8/10
= 2/10.5/8+8/10
= 1/8 + 4/5 = 5/40 + 32/40 = 37/40
b/ 0,5:5/4-2+1/5
= 5/10:5/4-11/5
= 5/10.4/5-11/5
=2/5-11/5 = -9/5
TL
1
NV
5 tháng 4 2017
Ta có: \(N=\dfrac{5}{3.5}-\dfrac{5}{5.7}-\dfrac{5}{7.9}-\dfrac{5}{9.11}-\dfrac{5}{11.13}-\dfrac{5}{13.15}
\)
\(\Rightarrow N=5\left(\dfrac{1}{3.5}-\dfrac{1}{5.7}-\dfrac{1}{7.9}-\dfrac{1}{9.11}-\dfrac{1}{11.13}-\dfrac{1}{13.15}\right)\)
\(\Rightarrow N=\dfrac{5}{2}\left(\dfrac{1}{3}+\dfrac{1}{5}-\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{7}+\dfrac{1}{9}-\dfrac{1}{9}+\dfrac{1}{11}-\dfrac{1}{11}+\dfrac{1}{13}-\dfrac{1}{13}+\dfrac{1}{15}\right)\)
\(\Rightarrow N=\dfrac{5}{2}\left(\dfrac{1}{3}+\dfrac{1}{15}\right)=\dfrac{5}{2}\left(\dfrac{5+1}{15}\right)=\dfrac{5}{2}.\dfrac{6}{15}\)
\(\Rightarrow N=\dfrac{3}{3}=1\)
Đặt 2/5 ra ngoài rồi tách từng cặp phân số ra sau đó bn tự làm nhé!
A=\(\frac{5}{5.7}+\frac{5}{7.9}+.........+\frac{5}{59.61}\)
=\(\frac{5}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+.........+\frac{2}{59.61}\right)\)
=\(\frac{5}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...........+\frac{1}{59}-\frac{1}{61}\right)\)
=\(\frac{5}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)\)
=\(\frac{5}{2}.\frac{56}{305}\)
=\(\frac{28}{61}\)