\(S=3+\frac{3}{2}+...+\frac{3}{2^9}\)
\(\Rightarrow S=3.\left(1+\frac{1}{2}+...+\frac{1}{2^9}\right)\)
Đặt \(A=1+\frac{1}{2}+...+\frac{1}{2^9}\)
\(\Rightarrow2A=2+1+...+\frac{1}{2^8}\)
\(\Rightarrow2A-A=\left(2+1+...+\frac{1}{2^8}\right)-\left(1+\frac{1}{2}+...+\frac{1}{2^9}\right)\)
\(\Rightarrow A=2-\frac{1}{2^9}\)
Lại có :
\(S=3.A\)
\(\Rightarrow S=3.\left(2-\frac{1}{2^9}\right)\)
\(\Rightarrow S=6-\frac{3}{2^9}\)
Vậy \(S=6-\frac{3}{2^9}\)
Chúc bạn học tốt !!!
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