Tính tổng S=3+3/2+3/2^2+3/2^3+...3/2^9
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Tính tổng ; S=3+ 3/2+3/2^2+...+3/2^9
\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}=3\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)\)
\(=3\left(2-1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{2^2}+...+\frac{1}{2^8}-\frac{1}{2^9}\right)=3\left(2-\frac{1}{2^9}\right)=6-\frac{3}{2^9}\)
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Tính tổng S=3+3/2+3/2^2+...+3/2^9
\(S=3\left(1+\frac{1}{2^{ }}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)\)
\(2S=3\left(\frac{2}{2^0}+\frac{2}{2^1}+\frac{2}{2^2}+...+\frac{2}{2^9}\right)=3\left(2+1+\frac{1}{2^{ }}+...+\frac{1}{2^8}\right)\)\(2S-S=S=3\left(2+1+\frac{1}{2^1}+...+\frac{1}{2^8}\right)-3\left(1+\frac{1}{2^1}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)=3.\left(2-\frac{1}{2^9}\right)=3.\frac{2^{10}-1}{2^9}\)
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tính tổng:
S=3+3/2+3/2^2+3/2^3+.....+3/2^9
Tính tổng S :
S=3/2+3/2^2+...+3/2^9
ta có :
2.S=\(\frac{3}{2^2}+\frac{3}{2^3}+...+\frac{3}{2^{10}}\)
2.S-S=\(\left(\frac{3}{2^2}+\frac{3}{2^3}+...+\frac{3}{2^{10}}\right)-\left(\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)
=>S=\(\frac{3}{2^{10}}-\frac{3}{2}\)
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Tính tổng :
S = 3 + 3/2 + 3/2^2 + ... + 3/2^9
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Tính tổng S=3+3/2+3/22+...+3/29
\(S=3+\frac{3}{2}+\frac{3}{2^2}+....+\frac{3}{2^9}\)
\(S=3.\left(1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^9}\right)\)
Đặt \(N=1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^9}\)
\(\Rightarrow2N-N=\left(2+1+\frac{1}{2}+...+\frac{1}{2^8}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^9}\right)\)
\(\Rightarrow N=2-\frac{1}{2^9}\)
Khi đó \(S=3.N=3.\left(2-\frac{1}{2^9}\right)=6-\frac{3}{2^9}=\frac{3069}{512}\)
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Tính tổng S=3+3\2+3\22+...+3\29
Tính tổng: S=3+3/2+3/22+...+3/29
tính tổng: S=3+3/2+3/22+....+3/29
\(2S=\left(3+\frac{3}{2}+...+\frac{3}{2^9}\right)\)
\(2S=6+3+...+\frac{3}{2^8}\)
\(2S-S=\left(6+3+...+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)
\(S=6-\frac{3}{2^9}\)
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\(2S=\left(3+\frac{3}{2}+...+\frac{3}{2^9}\right)\)
\(2S=6+3+...+\frac{3}{2^8}\)
\(2S-S=\left(6+3+...+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)
\(S=6-\frac{3}{2^9}\)
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