Ta có \(H=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+....+\frac{1}{2187}\)
Suy ra \(3H=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+....+\frac{1}{729}\)
Nên \(3H-H=1-\frac{1}{2187}\)hay \(2H=1-\frac{1}{2187}\)
Do đó \(H=\frac{1}{2}-\frac{1}{4374}=\frac{1093}{2187}\)
Vậy \(H=\frac{1093}{2187}\)
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