Question

chung to A=1/4+1/16+.....+1/576<1/2

Answer 1

\(A=\frac{1}{4}+\frac{1}{16}+....+\frac{1}{576}\)

\(\Rightarrow4A=1+\frac{1}{4}+....+\frac{1}{144}\)

\(\Rightarrow4A-A=1-\frac{1}{576}\)

\(\Rightarrow3A=1-\frac{1}{576}\)

\(\Rightarrow A=\frac{1-\frac{1}{576}}{3}\)

Ta có: \(\frac{1-\frac{1}{576}}{3}< \frac{1}{3}< \frac{1}{2}\)

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Answer 2

 

A=14 +116 +....+1576 

⇒4A=1+14 +....+1144 

⇒4A−A=1−1576 

⇒3A=1−1576 

⇒A=1−1576 3 

Ta có: 1−1576 3 <13 <12 

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