1/3*5+1/5*7+....+1/19*21
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NT
1
17 tháng 7 2015
\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}+\frac{1}{21.23}\)
\(A=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}+\frac{2}{21.23}\right)\)
\(A=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}+\frac{1}{21}-\frac{1}{23}\right)\)
\(A=\frac{1}{2}\left(1-\frac{1}{23}\right)\)
\(A=\frac{1}{2}.\frac{22}{23}\)
\(A=\frac{11}{23}\)
22 tháng 12 2017
\(\frac{1}{1.3}\)+\(\frac{1}{3\cdot5}\)+................+\(\frac{1}{19.21}\)
Đặt A = \(\frac{1}{1.3}\)+\(\frac{1}{3\cdot5}\)+.............+\(\frac{1}{19.21}\)
Nhân cả 2 vế của A với 2 ta có :
2A = \(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+............+\(\frac{2}{19.21}\)
2A = \(\frac{1}{1}\)-\(\frac{1}{3}\)+ \(\frac{1}{3}\) - \(\frac{1}{5}\)+ ............ + \(\frac{1}{19}\)- \(\frac{1}{21}\)
2A = \(\frac{1}{1}\)- \(\frac{1}{21}\)
2A = \(\frac{20}{21}\)
A = \(\frac{20}{21}\): 2
A = \(\frac{10}{21}\)
5 tháng 3 2020
=1/1.3.5+1/3/5/7+1/5.7.9+......+1/17/19/21
=1/4.(5-1/1.3.5+7-3/3.5.7+.....+21-17/17/19/21
=1/4.(5/1.3.5-1/1.3.5+7/3.5.7-3/3.5.7+.....+21/17.19.21-17/17.19.21
=1/4.(1/1.3-1/3.5+1/3.5-1/5.7+.....+1/17.19-1/19.21)
=1/4.(1/3.1/21.17)
=1/4.3200/9603
= 800/9603
Chúc bạn học tốt^^
C
5 tháng 3 2020
Đặt \(A=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{17.19.21}\)
\(\Rightarrow4A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+...+\frac{4}{17.19.21}\)
\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+...+\frac{1}{17.19}-\frac{1}{19.21}\)
\(=\frac{1}{1.3}-\frac{1}{19.21}=\frac{44}{133}\)
\(\Rightarrow A=\frac{44}{133}\div4=\frac{11}{133}\)
NT
0
\(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}\)
\(=\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}\right)\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{21}\right)=\frac{1}{2}.\frac{7-1}{21}=\frac{1}{7}\)
\(\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{19\times21}\)
\(=\frac{1}{2}\times\left(\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{19\times21}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+..+\frac{1}{19}-\frac{1}{21}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(=\frac{1}{2}\times\frac{2}{7}\)
\(=\frac{1}{7}\)