✫¸.•°*”˜˜”*°•✫ Ṱђầภ Ḉђết ✫•°*”˜˜”*°•.¸✫ nhân A với 2 rồi phân tích như vậy được
\(A=\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+....+\frac{1}{37\cdot39}\)
\(2A=\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+....+\frac{2}{37\cdot39}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-......+\frac{1}{37}-\frac{1}{39}\)
\(2A=\frac{1}{3}-\frac{1}{39}=\frac{12}{39}=\frac{4}{13}\)
\(A=\frac{4}{13}:2=\frac{4}{13}\cdot\frac{1}{2}=\frac{2}{13}\)
Vậy \(A=\frac{2}{13}\)
Bài làm
\(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{37.39}\)
\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{37}-\frac{1}{39}\)
\(A=\frac{1}{3}-\frac{1}{39}\)
\(A=\frac{13}{39}-\frac{1}{39}=\frac{12}{39}\)
Vậy \(A=\frac{12}{39}\)
A =1/3.5+1/5.7 +1/7.9 + ... +1/37.39
2.A = 2/3.5+ 2/5.7+ ....+2/37.39
2.A = 1/3- 1/5+1/5-1/7 +....+1/37-1/39
= 1/3- 1/39
2.A= 13/39 -1/39
2.A= 12/39
A = 12/39: 2
A= 2/13
Vậy A= 2/13
\(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+........+\frac{1}{37.39}\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+.......+\frac{2}{37.39}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{37}-\frac{1}{39}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{39}\right)=\frac{1}{2}.\left(\frac{13}{39}-\frac{1}{39}\right)=\frac{1}{2}.\frac{12}{39}=\frac{1.12}{2.39}=\frac{6}{39}=\frac{2}{13}\)
Vậy \(A=\frac{2}{13}\)
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