Toán Lớp 7: Cho:
A = 1/2^2 + 1/2^3 + 1/2^6 + … + 1/2^100
CM: A < 1/3
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Toán Lớp 7: Cho:
A = 1/2^2 + 1/2^3 + 1/2^6 + … + 1/2^100
CM: A < 1/3
Comments ( 2 )
A = \dfrac{1}{{{2^2}}} + \dfrac{1}{{{2^4}}} + \dfrac{1}{{{2^6}}} + … + \dfrac{1}{{{2^{100}}}}\\
\Leftrightarrow {2^2}.A = 1 + \dfrac{1}{{{2^2}}} + \dfrac{1}{{{2^4}}} + … + \dfrac{1}{{{2^{98}}}}\\
\Leftrightarrow 4A – A = 3A = 1 – \dfrac{1}{{{2^{100}}}}\\
\Leftrightarrow A = \dfrac{1}{3} – \dfrac{1}{{{{3.2}^{100}}}} < \dfrac{1}{3}\\
Vậy\,A < \dfrac{1}{3}
\end{array}$