Question

[cherry girl]

So sánh 1/3 +1/3^2 +.......+1/3^9 và 1/2

Answer 1

[l҉o҉n҉g҉ d҉z҉]

Đặt A = \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+......+\frac{1}{3^9}\)

\(\Rightarrow3A=1+\frac{1}{3}+\frac{1}{3^2}+......+\frac{1}{3^8}\)

\(\Rightarrow3A-A=1-\frac{1}{3^9}\)

\(\Rightarrow2A=1-\frac{1}{3^9}\)

=> A = \(\frac{1-\frac{1}{3^9}}{2}\) 

Mà : \(1-\frac{1}{3^9}< 1\)

Nên : A < \(\frac{1}{2}\)

Answer 2

[nguyên hanh my]

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