Tính A biết :\(A=\frac{1}{21}+\frac{1}{77}+\frac{1}{165}+\frac{1}{285}+\frac{1}{437}\)
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NN
9
HN
4 tháng 7 2018
\(D=\frac{4}{21}+\frac{4}{77}+\frac{4}{165}+\frac{4}{285}+\frac{4}{437}+\frac{4}{621}\)
\(D=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+\frac{4}{15.19}+\frac{4}{19.23}+\frac{4}{23.27}\)
\(D=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}+\frac{1}{23}-\frac{1}{27}\)
\(D=\frac{1}{3}-\frac{1}{27}\)
\(D=\frac{9}{27}-\frac{1}{27}\)
\(D=\frac{8}{27}\)
4 tháng 7 2018
\(D=\frac{4}{21}+\frac{4}{77}+\frac{4}{165}+\frac{4}{285}+\frac{4}{437}+\frac{4}{621}\)
\(D=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+\frac{4}{15.19}+\frac{4}{19.23}+\frac{4}{23.27}\)
\(D=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}+\frac{1}{23}-\frac{1}{27}\)
\(D=\frac{1}{3}-\frac{1}{27}\)
\(D=\frac{8}{27}\)
_Chúc bạn học tốt_
30 tháng 1 2022
\(\Leftrightarrow x\cdot\left[\dfrac{1}{4}\left(\dfrac{4}{21}+\dfrac{4}{77}+\dfrac{4}{165}\right)+\dfrac{2}{19\cdot30}+\dfrac{2}{19\cdot34}\right]=\dfrac{3}{276}\)
\(\Leftrightarrow x\cdot\left[\dfrac{1}{4}\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}\right)+\dfrac{32}{4845}\right]=\dfrac{3}{276}\)
\(\Leftrightarrow x\cdot\dfrac{71}{969}=\dfrac{3}{276}\)
hay \(x=\dfrac{969}{6532}\)
18 tháng 6 2021
Tìm x :
x - 0,27 = \(\frac{73}{100}\)
x = \(\frac{73}{100}+0,27\)
x = 1
18 tháng 6 2021
Cậu P khó quá mik chưa nghĩ ra cách tính nhanh nhất !
Cậu tự giải nhé !
Hok tốt
11 tháng 6 2016
\(\frac{1}{21}+\frac{1}{77}+\frac{1}{165}+...+\frac{1}{n^2+4n}=\frac{56}{673}\)
<=> \(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{n.\left(n+4\right)}=\frac{56}{673}\)
<=> \(4.\left(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{n.\left(n+4\right)}\right)=4.\frac{56}{673}\)
<=> \(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{n\left(n+4\right)}=\frac{224}{673}\)
<=> \(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{n}-\frac{1}{n+4}=\frac{224}{673}\)
<=> \(\frac{1}{3}-\frac{1}{n+4}=\frac{224}{673}\)
<=> \(\frac{n+4-3}{3.\left(n+4\right)}=\frac{224}{673}\Leftrightarrow\frac{n}{3.\left(n+4\right)}=\frac{224}{673}\)
<=> 673n = 224.3(n+4)
<=> 673n = 224.3.n + 224.3.4
<=> 673n = 672n + 2688
<=> 673n - 672n = 2688
<=> n = 2688
HH
20 tháng 5 2017
\(A=\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{n^2+4n}=\frac{56}{673}\)
\(4A=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{15}+...+\frac{1}{n^2}-\frac{1}{4n}=\frac{56}{673}\)
\(\Rightarrow4A=\)
S
20 tháng 5 2017
\(\frac{1}{21}+\frac{1}{77}+\frac{1}{165}+...+\frac{1}{n^2+4n}=\frac{56}{673}\)
\(\Rightarrow\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{n\left(n+4\right)}=\frac{56}{673}\)
\(\Rightarrow\frac{1}{4}\left(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{n\left(n+4\right)}\right)=\frac{56}{673}\)
\(\Rightarrow\frac{1}{4}\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{n}-\frac{1}{n+4}\right)=\frac{56}{673}\)
\(\Rightarrow\frac{1}{4}\left(\frac{1}{3}-\frac{1}{n+4}\right)=\frac{56}{673}\)
\(\Rightarrow\frac{1}{3}-\frac{1}{n+4}=\frac{56}{673}:\frac{1}{4}\)
\(\Rightarrow\frac{1}{3}-\frac{1}{n+4}=\frac{224}{673}\)
\(\Rightarrow\frac{1}{n+4}=\frac{1}{3}-\frac{224}{673}\)
\(\Rightarrow\frac{1}{n+4}=\frac{1}{2019}\)
=> n + 4 = 2019
n = 2019 - 4
n = 2015
A = \(\frac{1}{21}+\frac{1}{77}+\frac{1}{165}+\frac{1}{285}+\frac{1}{437}\)
A = \(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+\frac{1}{15.19}+\frac{1}{19.23}\)
A = \(\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}\right)+\frac{1}{4}.\left(\frac{1}{7}-\frac{1}{11}\right)+\frac{1}{4}.\left(\frac{1}{11}-\frac{1}{15}\right)+\frac{1}{4}.\left(\frac{1}{15}-\frac{1}{19}\right)+\frac{1}{4}.\left(\frac{1}{19}-\frac{1}{23}\right)\)
A = \(\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}\right)\)
A = \(\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{23}\right)\)
A = \(\frac{1}{4}.\frac{20}{69}\)
A = \(\frac{5}{69}\)
A=\(\frac{5}{69}\)