Question

cho B= \(\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{2014}{5^{2015}}.\)\(CMR:B< \frac{1}{16}\)

Lm ơn giúp tớ vs, tớ sẽ tk cho mak

Answer 1

\(5B=\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+...+\frac{2014}{5^{2014}}\)

\(5B-B=4B=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{2014}}-\frac{1}{5^{2015}}< \frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{2014}}\)

Đặt \(A=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{2014}}\)

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

\(5A-A=4A=1-\frac{1}{5^{2014}}< 1\)

=>A<1/4

Ta có 4B<A<1/4

=>B<1/16( đpcm)

Answer 2

khó quá bạn ạ

Answer 3

LÀM XONG CÁI NÀY CHẮC MIK HỎNG TAY MẤT