\(\dfrac{1}{4}A=\dfrac{1}{2^3}+\dfrac{1}{2^5}+...+\dfrac{1}{2^{101}}\)
=>\(A\cdot\dfrac{-3}{4}=\dfrac{1}{2^{101}}-\dfrac{1}{2}=\dfrac{1-2^{100}}{2^{101}}\)
=>\(A=\dfrac{2^{100}-1}{2^{101}}:\dfrac{3}{4}=\dfrac{2^{100}-1}{3\cdot2^{99}}\)
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