Câu 1:
1/3x5 + 1/5x7 + 1/7x9 +......+ 1/997x999
1/1x3 + 1/3x5 + 1/5x7 + 1/7x9
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9) chia 2
=(1-1/9)chia 2
=8/9 chia 2
=4/9
1/3x5 + 1/5x7 + 1/7x9 + ... + 1/2009x2011
A = \(\dfrac{1}{3\times5}\) + \(\dfrac{1}{5\times7}\) + \(\dfrac{1}{7\times9}\)+...+ \(\dfrac{1}{2009\times2011}\)
A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\)+ \(\dfrac{2}{7\times9}\)+...+ \(\dfrac{1}{2009\times2011}\))
A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{9}\)+...+ \(\dfrac{1}{2009}\) - \(\dfrac{1}{2011}\))
A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{3}\) - \(\dfrac{1}{2011}\))
A = \(\dfrac{1}{2}\) \(\times\) \(\dfrac{2008}{6033}\)
A = \(\dfrac{1004}{6033}\)
\(\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{2}{7\times9}+..+\dfrac{1}{2009\times2011}\\ =\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{2009}-\dfrac{1}{2011}\\ =\dfrac{1}{3}-\dfrac{1}{2011}\)
Đến đây bn tự tính nhé.
\(\text {#DNamNgV}\)
\(\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}+...+\dfrac{1}{2009\times2011}\)
\(=\dfrac{1}{2}\times\left(\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+...+\dfrac{2}{2009\times2011}\right)\)
\(=\dfrac{1}{2}\times\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2009}-\dfrac{1}{2011}\right)\)
\(=\dfrac{1}{2}\times\left[\dfrac{1}{3}-\left(\dfrac{1}{5}-\dfrac{1}{5}\right)-\left(\dfrac{1}{7}-\dfrac{1}{7}\right)-...-\dfrac{1}{2011}\right]\)
\(=\dfrac{1}{2}\times\left(\dfrac{1}{3}-\dfrac{1}{2011}\right)\)
\(=\dfrac{1}{2}\times\dfrac{2008}{6033}\)
\(=\dfrac{1004}{6033}\)
1/3x5+1/5x7+1/7x9+........+1/99x101
Đặt A = 1/3.5 + 1/5.7 + 1/7.9 + ..... + 1/99.101
=> 2A = 2/3.5 + 2/5.7 + 2/7.9 + ..... + 2/99.101
=> 2A = 1/3 - 1/5 + 1/5 - 1/7 + ..... + 1/99 - 1/101
=> 2A = 1/3 - 1/101
=> 2A = 88/303
=> A = 44/303
1/3x5 + 1/5x7 + 1/7x9 +...+ 1/99x101
1/1x3+1/3x5+1/5x7+1/7x9
Đặt \(A=\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}\)
\(2A=\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+\frac{2}{7x9}\)
\(2A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{9}\)
\(2A=\frac{1}{1}-\frac{1}{9}=\frac{8}{9}\)
\(A=\frac{8}{9}.\frac{1}{2}=\frac{4}{9}\)
A= 1/(1x3) + 1/(3x5)+ 1/(5x7) + 1/(7x9) + 1/(9x11)
A x 2 = 2/(1x3) + 2/(3x5)+ 2/(5x7) + 2/(7x9) + 2/(9x11)
Nhận xét :
2/(1x3) = 1 - 1/3
2/(3x5) = 1/3 - 1/5
2/(5x7) = 1/5 - 1/7
2/(7x9) = 1/7 - 1/9
2/(9x11) = 1/9 - 1/11
A x 2 = 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11
A x 2 = 1 - 1/11
A x 2 = 10/11
A = 10/11 : 2 = 5/11
các bạn k mình nha!
A= 1/(1x3) + 1/(3x5)+ 1/(5x7) + 1/(7x9) + 1/(9x11)
A x 2 = 2/(1x3) + 2/(3x5)+ 2/(5x7) + 2/(7x9) + 2/(9x11)
Nhận xét :
2/(1x3) = 1 - 1/3
2/(3x5) = 1/3 - 1/5
2/(5x7) = 1/5 - 1/7
2/(7x9) = 1/7 - 1/9
2/(9x11) = 1/9 - 1/11
A x 2 = 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11
A x 2 = 1 - 1/11
A x 2 = 10/11
A = 10/11 : 2 = 5/11
1/3x5+1/5x7+1/7x9+...+1/999x1001
1/3x5+1/5x7+1/7x9+...+1/43x45
1/3-1/5+1/5-1/7+1/7-1/9+...+1/43-1/45
=1/3-1/45
=14/45
1/1x3+1/3x5+1/5x7+1/7x9 = ?
Coi A=1/1x3+1/3x5+1/5x7+1/7x9
=>2A=2x(1/1x3+1/3x5+1/5x7+1/7x9)=2/1x3+2/3x5+2/5x7+2/7x9
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9
=1-1/9=8/9
=>A=8/9:2=4/9
1/3x5+1/5x7+1/7x9+1/9x11+1/11x13
\(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+\frac{1}{9x11}+\frac{1}{11x13}\)
\(=\frac{1}{2}x\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{1}{2}x\left(\frac{1}{3}-\frac{1}{13}\right)\)
\(=\frac{1}{2}x\frac{10}{39}\)
\(=\frac{5}{39}\)
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}\)
\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{13}\right)\)
\(=\frac{1}{2}\cdot\frac{10}{39}=\frac{5}{39}\)
Đặt A=\(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+...+\frac{1}{11x13}\)
Ax2=\(2x\left(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+...+\frac{1}{11x13}\right)\)
Ax2=\(\frac{2}{3x5}+\frac{2}{5x7}+\frac{2}{7x9}+...+\frac{2}{11x13}\)
Ax2=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)
Ax2=\(\frac{1}{3}-\frac{1}{13}\)
Ax2=\(\frac{10}{39}\)
=>A=\(\frac{5}{39}\)
~~~hok tốt~~~