2/11x13 + 2/13x15 + . . . . . . .+2/19x21
vẫn là tính nhanh
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NH
3
25 tháng 7 2016
\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.........+\frac{1}{13}-\frac{1}{15}\)
\(=1-\frac{1}{15}\)
\(=\frac{14}{15}\)
NV
11 tháng 6 2018
\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\)\(...+\frac{2}{8.9}+\frac{2}{9.10}\)
Đặt \(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)
\(B=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{8.9}+\frac{2}{9.10}\)
Ta có:
\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)
\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)
\(A=\frac{1}{3}-\frac{1}{15}\)
\(A=\frac{4}{15}\)
\(B=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{8.9}+\frac{2}{9.10}\)
\(B=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(B=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(B=2\left(1-\frac{1}{10}\right)\)
\(B=2.\frac{9}{10}\)
\(B=\frac{9}{5}\)
\(\Rightarrow A+B=\frac{4}{15}+\frac{9}{5}\)
\(=\frac{31}{15}\)
Vậy biểu thức trên có giá trị là \(\frac{31}{15}\)
22 tháng 3
=2/5-2/7+ 2/7-2/9+2/9-2/11+2/11-2/13+2/13-2/15
=2/5-(2/7-2/7)-(2/9-2/9)-(2/11-2/11)-(2/13-2/13)-2/15
=2/5-0-0-0-0-2/15
=2/5-2/15
4/15
W
4
1 tháng 4 2017
2/11x13+2/13x15+2/15x17+...+2/97x99
=1/11-1/13+1/13-1/15+1/15-1/17+...+1/97-1/99
=1/11-1/99
=8/99
BH
0
25 tháng 10 2023
\(\dfrac{4}{9\cdot11}+\dfrac{4}{11\cdot13}+...+\dfrac{4}{97\cdot99}\)
\(=2\left(\dfrac{2}{9\cdot11}+\dfrac{2}{11\cdot13}+...+\dfrac{2}{97\cdot99}\right)\)
\(=2\left(\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=2\cdot\left(\dfrac{1}{9}-\dfrac{1}{99}\right)\)
\(=2\cdot\dfrac{10}{99}=\dfrac{20}{99}\)
DG
0
DG
2
DP
11 tháng 6 2017
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
Ta có:
\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+....+\frac{1}{19}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(\left(\frac{1}{11}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(\frac{10}{231}-x+\frac{221}{231}=\frac{4}{3}\)
\(\frac{10}{231}-x=\frac{4}{3}-\frac{221}{231}=\frac{29}{77}\)
\(x=\frac{10}{231}-\frac{29}{77}\)
\(x=-\frac{1}{3}\)
CW
28 tháng 4 2018
2/(11x13) = 1/11 - 1/13 ; 2/(13x15) = 1/13 - 1/15 ; 2/(15x17) = 1/15 - 1/17 ; 2/(17x19) = 1/17 - 1/19 ; 2/(19x21) = 1/19 - 1/21
2/(11x13) + 2/(13x15) + 2/(15x17) + 2/(17x19) 2/(19x21) =
1/11 - 1/13 + 1/13 - 1/15 + 1/15 - 1/17 + 1/17 - 1/19 + 1/19 - 1/21 = 1/11 - 1/21 = 101231
Hay: 10/231 x 462 - X = 19
20 - X = 19
X = 20 - 19
X = 1
=1/11 - 1/13 + 1/13 - 1/15 +...+1/19 - 1/21
=1/11-1/21=10/231