5/3.7+5/7.11+...+5/(4n-1).(4n+3)=5/4n+3
K
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K
1
29 tháng 6 2016
\(A=\frac{5}{3.7}+\frac{5}{7.11}+...+\frac{5}{\left(4n-1\right).\left(4n+3\right)}\)
\(\frac{4}{5}.A=\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{\left(4n-1\right).\left(4n+3\right)}\)
\(\frac{4}{5}.A=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{4n-1}-\frac{1}{4n+3}\)
\(\frac{4}{5}.A=\frac{1}{3}-\frac{1}{4n+3}\)
\(\frac{4}{5}.A=\frac{4n+3}{12n+9}-\frac{3}{12n+9}\)
\(\frac{4}{5}.A=\frac{4n}{12n+9}\)
\(A=\frac{4n}{12n+9}:\frac{4}{5}\)
\(A=\frac{4n}{12n+9}.\frac{5}{4}\)
\(A=\frac{5n}{12n+9}\)
Đề bài sai nha bn
Ủng hộ mk nha ^_^
J
2 tháng 7 2018
\(\dfrac{5}{3\cdot7}+\dfrac{5}{7\cdot11}+\dfrac{5}{11\cdot15}+...+\dfrac{5}{\left(4n-1\right)\left(4n+3\right)}\\ =\dfrac{5}{4}\cdot\left(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{4}{11\cdot15}+...+\dfrac{4}{\left(4n-1\right)\left(4n+3\right)}\right)\\ =\dfrac{5}{4}\cdot\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+...+\dfrac{1}{4n-1}-\dfrac{1}{4n+3}\right)\\ =\dfrac{5}{4}\cdot\left(\dfrac{1}{3}-\dfrac{1}{4n+3}\right)\\ =\dfrac{5}{4}\cdot\dfrac{4n}{12n+9}\\ =\dfrac{5n}{12n+9}\)
Mk thực sự nghĩ đề hình như bị sai hay sao ấy!
28 tháng 1 2016
=\(\frac{5}{4}\left(\frac{4}{3.7}+\frac{4}{7.11}+........+\frac{4}{\left(4n-1\right)\left(4n+3\right)}\right)\)
\(=\frac{5}{4}\left(\frac{7-3}{7.3}+\frac{11-7}{7.11}+........+\frac{\left(4n+3\right)-\left(4n-1\right)}{\left(4n-1\right)\left(4n+3\right)}\right)\)
\(=\frac{5}{4}\left(\frac{7}{7.3}-\frac{3}{7.3}+\frac{11}{7.11}-\frac{7}{7.11}+......+\frac{4n+3}{\left(4n-1\right)\left(4n+3\right)}-\frac{4n-1}{\left(4n-1\right)\left(4n+3\right)}\right)\)
\(=\frac{5}{4}\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7.}-\frac{1}{11}+......+\frac{1}{4n-1}-\frac{1}{4n+3}\right)\)
\(=\frac{5}{4}\left(\frac{1}{3}-\frac{1}{4n+3}\right)\)
\(=\frac{5}{4}\left(\frac{4n+3}{3\left(4n+3\right)}-\frac{3}{3\left(4n+3\right)}\right)\)
\(=\frac{5}{4}\left(\frac{4n+3-3}{3\left(4n+3\right)}\right)\)
\(=\frac{5}{4}.\frac{4n}{3\left(4n+3\right)}=\frac{4.n.5}{3\left(4n+3\right).4}=\frac{5n}{3\left(4n+3\right)}\)
ban nen xem lai dau bai di minh giai dung 100% do
ma neu dau bai ra nhu ket qua cua to thi tick cho minh nha
nếu lm sai thì thôi na
đặt vế trái lak A
4A=5(5/3.7+5/7.11+.....+5/(4n-1)(4n+3)
4A=(1/3-1/4n+3)
4A=4n+3-3/3(4n+3)
4A=4/12n+9
A=5/4n+3
bn ở đâu