A = 1.3.5 + 3.5.7 + 5.7.9 + ..... + 45.47.49 + 47.49.51
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Đặt A = 1.3.5 + 3.5.7 + 5.7.9 + ...... + 47.49.51
8A = 1.3.5.8 + 3.5.7.8 + ...... + 47.49.51.8
= 1.3.5(7 + 1) + 3.5.7.(9 - 1) + ...... + 47.49.51(53 - 45)
= 1.3.5.7 + 1.3.5 + 3.5.7.9 - 1.3.5.7 + ......... + 47.49.51.53 - 47.47.49.51
= 1.3.5 + 47.49.51.53
=> A = \(\frac{1.3.5+47.49.51.53}{8}=778128\)
\(=\frac{1}{4}.\left(\frac{17.4}{1.3.5}+\frac{17.4}{3.5.7}+\frac{17.4}{5.7.9}+...+\frac{17.4}{47.49.51}\right)\)
\(=\frac{17}{4}\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{47.49}-\frac{1}{49.51}\right)\)
\(=\frac{17}{4}\left(\frac{1}{3}-\frac{1}{2499}\right)=\frac{17}{4}.\frac{832}{2499}=\frac{208}{147}\)
\(\Rightarrow\) 8A= 1.3.5.8 + 3.5.7.8 + 5.7.9.8 + ................ + 95.97.99.8
\(\Rightarrow\) 8A=1.3.5(7+1)+3.5.7(9-1)+5.7.9.(11-3)+.......+95.97.99(101-93)
\(\Rightarrow\) 8A=1.3.5.7+15+3.5.7.9-3.5.7+5.7.9.11-3.5.7.9+.......+95.97.99.101- 93.95.97.99
\(\Rightarrow\) 8A=15+95.97.99.101
\(\Rightarrow\) A=(15+95.97.99.101):8
\(\Rightarrow\) A=11517600 Vậy A = 11517600
A = 1 . 3 . 5 - 3. 5 . 7 + 5 . 7 . 9 - 7.9.11 + ... + 97.99.101
4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + … + 98.99.100.4
= 1.2.3.4 + 2.3.4(5 - 1) + 3.4.5(6 - 2) + … + 98.99.100(101 - 97)
= 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + … + 98.99.100.101 - 97.98.99.100
= 98.99.100.101
=> A = 98.99.25.101
A = 24 497 550
\(A=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{95.97.99}\)
\(A=4.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+...+\frac{1}{95.97}-\frac{1}{97.99}\right)\)
\(A=4.\left(\frac{1}{1.3}-\frac{1}{97.99}\right)\)
\(A=4.\frac{3200}{9603}=\frac{12800}{9603}\)
\(A=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{95.97.99}\)
\(A=\frac{1}{4}.\left(\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{95.97.99}\right)\)
\(A=\frac{1}{4}.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+...+\frac{1}{95.97}-\frac{1}{97.99}\right)\)
\(A=\frac{1}{4}.\left(\frac{1}{1.3}-\frac{1}{97.99}\right)\)
\(A=\frac{1}{4}.\frac{3200}{9603}\)
\(A=\frac{800}{9603}\)
Bài trc mik làm lộn :)))
~ Hok tốt ~
\(A=\frac{24}{1.3.5}+\frac{24}{3.5.7}+\frac{24}{5.7.9}+...+\frac{24}{25.27.29}\)
\(A=6\left(\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+...+\frac{4}{25.27.29}\right)\)
\(A=6\left(\frac{5-1}{1.3.5}+\frac{7-3}{3.5.7}+\frac{9-5}{5.7.9}+...+\frac{29-25}{25.27.29}\right)\)
\(A=6\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{25.27}-\frac{1}{27.29}\right)\)
\(A=6\left(\frac{1}{1.3}-\frac{1}{27.29}\right)=\frac{520}{261}\)