Đặt \(A=\frac32+\frac94+\cdots+\frac{897}{128}\)
\(=\frac{2+1}{2}+\frac{8+1}{4}+\cdots+\frac{896+1}{128}\)
\(=1+2+\cdots+7+\frac12+\frac{1}{2^2}+\cdots+\frac{1}{2^7}\)
\(=7\cdot\frac82+\left(\frac12+\frac{1}{2^2}+\cdots+\frac{1}{2^7}\right)\)
\(=28+\left(\frac12+\frac{1}{2^2}+\cdots+\frac{1}{2^7}\right)\)
Đặt \(B=\frac12+\frac{1}{2^2}+\cdots+\frac{1}{2^7}\)
=>\(2B=1+\frac12+\cdots+\frac{1}{2^6}\)
=>2B-B=\(1+\frac12+\cdots+\frac{1}{2^6}-\frac12-\frac{1}{2^2}-\cdots-\frac{1}{2^7}\)
=>\(B=1-\frac{1}{2^7}=\frac{127}{128}\)
=>\(A=28+\frac{127}{128}=\frac{3711}{128}\)
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