3/2+3/8+3/32+3/128+3/512
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
3/2 + 3/8 + 3/32 + 3/128 + 3/512
= 768/512 + 182/512 + 48/512 + 12/512 + 3/512
= 960/512 + 60/512 + 3/512
= 1023/512
![](https://rs.olm.vn/images/avt/0.png?1311)
\(...=\dfrac{3}{2}x\left(1+\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}\right)\)
\(=\dfrac{3}{2}x\left(\dfrac{256}{256}+\dfrac{64}{256}+\dfrac{16}{256}+\dfrac{4}{256}+\dfrac{1}{256}\right)\)
\(=\dfrac{3}{2}x\dfrac{341}{256}=\dfrac{1023}{512}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt tổng trên = A
\(A=\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}\)
\(A.4=6+\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}\)
\(A.4-A=\left(6+\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}\right)-\left(\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}\right)\)
\(A.3=6-\frac{3}{512}=\frac{3069}{512}\)
\(A=\frac{3069}{512}:3=\frac{1023}{512}\)
Đặt A = 3/2 + 3/8 + ... + 3/512
bn tách
3/2 = 3/2^1
3/8 = 3/2^3
...
3/512 = 3/2^9
Rồi nhân nó lên trừ được bao nhiêu - đi A ban đầu là đc
k nka
![](https://rs.olm.vn/images/avt/0.png?1311)
C = \(\dfrac{3}{2}\) + \(\dfrac{3}{4}\) + \(\dfrac{3}{8}\)+ \(\dfrac{3}{16}\)+...........+\(\dfrac{3}{128}\)
C\(\times\)2 = 3 + \(\dfrac{3}{2}\) + \(\dfrac{3}{4}\) + \(\dfrac{3}{8}\) + \(\dfrac{3}{16}\)+...+\(\dfrac{1}{64}\)
C\(\times\)2 - C = 3 - \(\dfrac{3}{128}\)
C = \(\dfrac{381}{128}\)
Câu E em xem lại đề nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt tổng trên là: \(A\)
\(A=\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}+\dfrac{3}{512}\)
\(\Rightarrow A.4=6+\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}\)
\(\Rightarrow A.4-A=\left(6+\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}\right)-\left(\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}+\dfrac{3}{512}\right)\)
\(\Rightarrow A.3=6-\dfrac{3}{512}=\dfrac{3069}{512}\)
\(\Rightarrow A=\dfrac{3069}{512}:3=\dfrac{1023}{512}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(P+\frac{1}{512}=\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{4}{512}=\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{4}{128}=\)
\(=\frac{3}{2}+\frac{3}{8}+\frac{4}{32}=\frac{3}{2}+\frac{4}{8}=\frac{4}{2}=2\)
\(\Rightarrow P=2-\frac{1}{512}=\frac{1023}{512}\)
\(P=\frac{3}{2}+\frac{3}{8}+...+\frac{3}{512}\)
\(=3.\left(\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\right)\)
\(4P=3\left(\frac{1}{2^3}+\frac{1}{2^5}+...+\frac{1}{2^{11}}\right)\)
\(4P-P=3\left(\frac{1}{2}-\frac{1}{2^{11}}\right)\)
\(3P=3\left(\frac{1}{2}-\frac{1}{2^{11}}\right)\)
\(P=\frac{1}{2}-\frac{1}{2^{11}}=\frac{2^{10}-1}{2^{11}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
đặt 3 ra ngoài,,,,đặt bên trong là A ,,rồi nhân A vs 1/2 ,,lấy A-1/2A=,,,,,,, đc bao nhiu chia 1/2