\(\frac{9}{11}=\frac{1}{a+\frac{1}{b+\frac{1}{c}}}\)
tim a,b,c
K
Khách
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31 tháng 8 2016
C = 1/100 - ( 1/2.1 + 1/3.2 + ... + 1/98.97 + 1/99.98 + 1/100.99
C = 1/100 - ( 1- 1/2+ 1/2 - 1/3 + ... + 1/97 - 1/98 + 1/98 - 1/99 + 1/99 - 1/100 )
C = 1/100 - ( 1 - 1/100 )
C = 1/100 - 99/100
C = \(\frac{-49}{50}\)
XO
3 tháng 4 2021
\(\left(a+b+c\right)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=1\)
=> \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}\)
=> \(\frac{1}{a}+\frac{1}{b}=\frac{1}{a+b+c}-\frac{1}{c}\)
=> \(\frac{a+b}{ab}=\frac{-\left(a+b\right)}{\left(a+b+c\right).c}\)
Khi a + b = 0
=> (a + b)(b + c)(c + a) = 0 (2)
Nếu a + b \(\ne0\)
=> ab = -(a + b + c).c
=> ab + (a + b + c).c = 0
=> ab + ac + bc + c2 = 0
=> (a + c)(b + c) = 0
=> (a + b)(b + c)(a + c) = 0 (1)
Từ (2)(1) => (a + b)(b + c)(a + c) = 0 \(\forall a;b;c\)
=> a = -b hoặc b = -c hoặc = c = -a
Nếu a = -b => a11 = -b11 => a11 + b11 = 0
=> P = 0 (3)
Nếu b = -c => b9 = - c9 => b9 + c9 = 0
=>P = 0 (4)
Nếu c = -a => c2001 = -a2001 => c2001 + a2001 = 0
=> P = 0 (5)
Từ (3);(4);(5) => P = 0 trong cả 3 trường hợp
Vạy P = 0
29 tháng 1 2022
a: \(A=\dfrac{-3}{8}\left(16+\dfrac{8}{17}+7+\dfrac{9}{17}\right)=\dfrac{-3}{8}\cdot24=-9\)
b: \(B=\dfrac{\dfrac{3}{5}-\dfrac{3}{9}+\dfrac{3}{11}}{\dfrac{7}{5}-\dfrac{7}{9}+\dfrac{7}{11}}=\dfrac{3}{7}\)
IM
1 tháng 8 2016
a)
\(A=\left(\frac{1}{9}-\frac{1}{10}\right)-\left(\frac{1}{8}-\frac{1}{9}\right)-....-\left(1-\frac{1}{2}\right)=\frac{1}{9}-\frac{1}{10}-\frac{1}{8}+\frac{1}{9}-....-1+\frac{1}{2}\)
\(A=-\left(\frac{1}{10}+1\right)=-\frac{11}{10}\)
YN
21 tháng 2 2017
a)\(A=\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\\ \Rightarrow A=-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}-\frac{1}{42}-\frac{1}{56}-\frac{1}{72}-\frac{1}{90}\\ \Rightarrow A=-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)Đặt \(B=\frac{1}{2}+\frac{1}{6}+...+\frac{1}{72}+\frac{1}{90}\)
\(\Rightarrow B=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\)
\(\Rightarrow B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(\Rightarrow B=1-\frac{1}{10}=\frac{9}{10}\)
Ta có : \(A=-B\)
\(\Rightarrow A=-\frac{9}{10}\)
IM
20 tháng 2 2017
a) Ta có :
\(A=\frac{\frac{2}{5}-\frac{2}{9}+\frac{2}{11}}{\frac{7}{5}-\frac{7}{9}+\frac{7}{11}}\)
\(A=\frac{2\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}{7\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}\)
\(A=\frac{2}{7}\)
b) Ta có :
\(B=\frac{\frac{1}{3}-\frac{1}{4}+\frac{1}{5}}{\frac{7}{6}-\frac{7}{8}+\frac{7}{10}}\)
\(B=\frac{\frac{1}{3}-\frac{1}{4}+\frac{1}{5}}{\frac{7}{2}\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{5}\right)}\)
\(B=\frac{2}{7}\)
\(\Rightarrow\frac{A}{B}=\frac{\frac{2}{7}}{\frac{2}{7}}=1\)
14 tháng 8 2018
a )( 2/5+2/9-2/11)/(8/5+8/9-8/11)=2*(1/5+1/9-1/11)/8*(1/5+1/9-1/11)=2/8=1/4
10 tháng 4 2019
a) \(\frac{5}{9}:\frac{13}{7}+\frac{5}{9}:\frac{13}{9}-1\frac{2}{3}\\ =\frac{5}{9}\cdot\frac{7}{13}+\frac{5}{9}\cdot\frac{9}{13}-\frac{5}{3}\\ =\frac{5}{9}\left(\frac{7}{13}+\frac{9}{13}\right)-\frac{5}{3}\\ =\frac{5}{9}\cdot\frac{16}{13}-\frac{5}{3}\\ =\frac{80}{117}-\frac{5}{3}\\ =\frac{80}{117}-\frac{195}{117}=\frac{-115}{117}\)
b) \(\left(15-6\frac{13}{18}\right):11\frac{1}{27}-2\frac{1}{8}:1\frac{11}{40}\\ =\left(\frac{270}{18}-\frac{121}{18}\right):\frac{298}{27}-\frac{17}{8}:\frac{51}{40}\\ =\frac{149}{18}\cdot\frac{27}{298}-\frac{17}{8}\cdot\frac{40}{51}\\ =\frac{3}{4}-\frac{5}{3}\\ =\frac{9}{12}-\frac{20}{12}=\frac{-11}{12}\)
Ta có:\(\frac{9}{11}\)=\(\frac{1}{\frac{11}{9}}\)=\(\frac{1}{1+\frac{2}{9}}\)=\(\frac{1}{1+\frac{1}{\frac{9}{2}}}\)=\(\frac{1}{1+\frac{1}{4+\frac{1}{2}}}\).Từ đó suy ra:a=1;b=4;c=2