Question

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

Answer 1

TỪ ĐỀ BÀI => 5A=1+1/5+1/5^2+......+1/5^2013

                      CÓ 4A=5A-A

                    =>4A=(1+1/5+1/5^2+.....+1/5^2013)-(1/5+1/5^2+1/5^3+....+1/5^2014)

                   =>4A= 1- 1/5^2014

                   =>A= (1-1/5^2014)/4  ;CÓ 1-1/5^2014 <1

                    =>A<1/4

Answer 2

\(\text{Giải}\)

\(\text{5A=1+1/5+1/5^2+......+1/5^2013}\)

\(\Rightarrow5A-A=4A=1-\frac{1}{5^{2014}}< 1\Rightarrow A< \frac{1}{4}\left(\text{đpcm}\right)\)