Question

Cho A =  1/5 + 1/5^2 + 1/5^3 +....+ 1/5^2014 . Chứng tỏ rằng A < 1/4 

Answer 1

\(A=\frac{1}{5}+\frac{1}{5^2}+........+\frac{1}{5^{2014}}\)

\(\Rightarrow5A=1+\frac{1}{5}+...........+\frac{1}{5^{2013}}\)

\(\Rightarrow5A-A=1+...........+\frac{1}{5^{2013}}-\frac{1}{5}+...........+\frac{1}{5^{2014}}\)

\(\Rightarrow4A=1-\frac{1}{5^{2014}}\)

\(\Rightarrow4A< 1\Rightarrow A< \frac{1}{4}\)

Answer 2

=> 5A = 1 + 1/5 +...+1/5^2013

=>4A= 1- 1/5^2014

=> 4A< 1 => A < 1/4