Tính :
A = \(\left(\frac{1}{11x13}+\frac{1}{13x15}+\frac{1}{15x17}+......+\frac{1}{19x21}\right)\)
K
Khách
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DP
6 tháng 8 2017
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right)\cdot462-x=19\)
\(\Rightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)\cdot462-x=19\)
\(\Rightarrow\left(\frac{1}{11}-\frac{1}{21}\right)\cdot462-x=19\)
\(\Rightarrow\frac{10}{231}\cdot462-x=19\)
\(\Rightarrow20-x=19\Rightarrow x=1\)
TP
6 tháng 8 2017
Ta có:
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right).462-x=19\)
\(\Rightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right).462-x=19\)
\(\Rightarrow\left(\frac{1}{11}-\frac{1}{21}\right).462-x=19\)
\(\Rightarrow\frac{10}{231}.462-x=19\Leftrightarrow20-x=19\)
\(\Rightarrow x=20-19=1\)
PT
Tìm y biết \(\left(\frac{2}{11x13}+\frac{2}{13x15}+\frac{2}{15x17}+\frac{2}{17x19}\right)+462-y=19\)
1
2 tháng 3 2016
ta lấy : (1/11-1/13+1/13-1/15+...+1/19)x462-y=19
(1/11-1/19)x462-y=19
32/209x462-y=19
70,73-y=19
y=70,73-19=51,73
đúng thì k cho mình nhé , ko đúng cũng ko sao ^^
4 tháng 7 2018
\(\frac{3}{11\text{x}13}+\frac{3}{13\text{x}15}+\frac{3}{15\text{x}17}+\frac{3}{17\text{x}19}+\frac{3}{19\text{x}21}\)
\(=\frac{3}{2}\text{x}\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right)\)
\(=\frac{3}{2}\text{x}\left(\frac{1}{11}-\frac{1}{21}\right)\)
\(=\frac{3}{2}\text{x}\frac{10}{231}\)
\(=\frac{5}{77}\)
DP
15 tháng 6 2017
1. \(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right)\times462-x=19\)
\(\left(\frac{13-11}{11.13}+\frac{15-13}{13.15}+\frac{17-15}{15.17}+\frac{19-17}{17.19}+\frac{21-19}{19.21}\right)\times462-x=19\)
\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right)\times462-x=19\)
\(\left(\frac{1}{11}-\frac{1}{21}\right)\times462-x=19\)
\(\frac{10}{231}\times462-x=19\)
\(20-x=19\)
\(x=20-19\)
\(x=1\)
21 tháng 8 2018
2.b \(187-[[497-(8\times x+11)\div x]\div3-78]=150\)
\(187-[[497-(\frac{8\times x}{x}+\frac{11}{x})]:3-78]=150\)
\(187-[(497-8-\frac{11}{x}):3-78]=150\)
\(187-[(489-\frac{11}{x}):3-78]=150\)
\(187-[\frac{489}{3}-\frac{33}{x}-78]=150\)
\(187-[163-\frac{33}{x}-78]=150\)
\(187-85+\frac{33}{x}=150\)
\(102+\frac{33}{x}=150\)
\(\frac{33}{x}=150-102\)
\(\frac{33}{x}=48\)
\(x=\frac{48}{33}=\frac{16}{11}\)
NP
7
23 tháng 6 2017
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right).462-x=19\)
\(\left(\frac{1}{11}-\frac{1}{13}+...+\frac{1}{19}-\frac{1}{21}\right)\cdot462-x=19\)
\(\left(\frac{1}{11}-\frac{1}{21}\right)\cdot462-x=19\)
\(\frac{10}{231}.462-x=19\)
\(20-x=19\)
\(x=20-19\)
\(x=1\)
23 tháng 6 2017
Đề abfi sai. Chỗ đó là 19, k phải 29
Bạn biết tính chất này không?
\(\frac{a}{n\left(n+a\right)}=\frac{1}{n}-\frac{1}{n+a}\)
Sử dụng tính chất đó thì được:
\(\left(\frac{2}{11}-\frac{2}{13}+\frac{2}{13}-\frac{2}{15}+...+\frac{2}{19}-\frac{2}{21}\right)\)x 462 - x =19
\(\left(\frac{2}{11}-\frac{2}{21}\right)\cdot462-x=19\)
\(\frac{924}{11}-\frac{924}{21}-x=19\)
84 - 44 - x =19
40 - x = 19
x = 40 - 19
x = 21
Nhớ tk cho mình nếu đúng nhé
NA
2
CL
24 tháng 4 2016
A=\(\frac{4}{11}-\frac{4}{13}+\frac{4}{13}-\frac{4}{15}+...+\frac{4}{99}-\frac{4}{101}\)
\(A=4\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(A=4.\left(\frac{1}{11}-\frac{1}{101}\right)\)
A=4. 90/1111=360/1111
BH
0
\(A=\frac{1}{11.13}+\frac{1}{13.15}+..+\frac{1}{19.21}\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+..+\frac{1}{19}-\frac{1}{21}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{21}\right)\)
\(A=\frac{1}{11\cdot13}+\frac{1}{13\cdot15}+...+\frac{1}{19\cdot21}\)
\(2A=\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+...+\frac{2}{19\cdot21}\)
\(2A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\)
\(2A=\frac{1}{11}-\frac{1}{21}+0+...+0\)
\(2A=\frac{10}{231}\)
\(A=\frac{5}{231}\)