1/5x7 + 1/7x9 + 1/9x11 +………1/97x99
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YS
2 tháng 2 2018
Ta có: A = \(\frac{6}{5\times7}+\frac{6}{7\times9}+\frac{6}{9\times11}+...+\frac{6}{95\times97}+\frac{6}{97\times99}\)
\(\Rightarrow A=\frac{1}{6}\left(\frac{1}{5\times7}+\frac{1}{7\times9}+\frac{1}{9\times11}+...+\frac{1}{95\times97}+\frac{1}{97\times99}\right)\)
\(\Rightarrow A=\frac{1}{6}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{95}-\frac{1}{97}+\frac{1}{97}-\frac{1}{99}\right)\)
\(\Rightarrow A=\frac{1}{6}\left(\frac{1}{5}-\frac{1}{99}\right)\)
=> A = ...
KT
15 tháng 10 2018
\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)
\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)
\(=9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)
\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
\(=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)
\(=9-\left(1-\frac{1}{10}\right)\)
\(=9-\frac{9}{10}=\frac{81}{10}\)
31 tháng 5 2018
\(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+\frac{1}{9x11}+\frac{1}{11x13}\)
\(=\frac{1}{2}x\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{1}{2}x\left(\frac{1}{3}-\frac{1}{13}\right)\)
\(=\frac{1}{2}x\frac{10}{39}\)
\(=\frac{5}{39}\)
31 tháng 5 2018
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}\)
\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{13}\right)\)
\(=\frac{1}{2}\cdot\frac{10}{39}=\frac{5}{39}\)
14 tháng 7 2016
1/1 x 3 + 1/3 x 5 + 1/5 x 7 + 1/7 x 9 + 1/9 x 11
= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11
= 1 - 1/11
= 10/11
18 tháng 8 2015
\(\frac{1}{1.3}+\frac{1}{3.5}+....+\frac{1}{9.11}=\frac{1}{2}\left(\frac{2}{1.3}+\frac{1}{3.5}+....+\frac{2}{9.11}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{11}\right)=\frac{1}{2}.\left(1-\frac{1}{11}\right)\)
\(=\frac{1}{2}.\frac{10}{11}=\frac{5}{11}\)
6 tháng 6 2016
Đặt A = 1/3×5 + 1/5×7 + 1/7×9 + ... + 1/97×99
2A = 2/3×5 + 2/5×7 + 2/7×9 + ... + 2/97×99
2A = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ... + 1/97 - 1/99
2A = 1/3 - 1/99
2A = 32/99
A = 32/99 : 2
A = 32/99 × 1/2 = 16/99
LV
0
VA
7 tháng 7 2016
Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)
\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
\(2A=1-\frac{1}{9.11}=1-\frac{1}{99}=\frac{98}{99}\)
\(A=\frac{98}{99}:2=\frac{49}{99}\)
Ủng hộ mk nha!!!
HT
4 tháng 11 2015
A = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
A = \(\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
A = \(\frac{1}{2}.\left(1-\frac{1}{11}\right)=\frac{1}{2}.\frac{10}{11}\)
A = \(\frac{5}{11}\)
M
27 tháng 6 2019
1/5*7 + 1/7*9 + 1/9*11 + ... + 1/13*15
= 1/2(2/5*7 + 2/7*9 + 2/9*11 + ... + 2/13*15)
= 1/2(1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13 + 1/13 - 1/15)
= 1/2(1/5 - 1/15)
= 1/2.2/15
= 1/15
27 tháng 6 2019
Bài giải
\(\text{Đặt }A=\frac{1}{5\text{ x }7}+\frac{1}{7\text{ x }9}+\frac{1}{9\text{ x }11}+\frac{1}{11\text{ x }13}+\frac{1}{13\text{ x }15}\)
\(A=\frac{1}{2}\left(\frac{2}{5\text{ x }7}+\frac{2}{7\text{ x }9}+\frac{2}{9\text{ x }11}+\frac{2}{11\text{ x }13}+\frac{2}{13\text{ x }15}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{15}\right)\)
\(A=\frac{1}{2}\cdot\frac{2}{15}\)
\(A=\frac{1}{15}\)
=1/5-1/7 + 1/7 - 1/9 + 1/9 - 1/11+....+1/97-1/99
=1/5 -1/99
=....