Question

cho A =\(\frac{1}{2^2}\)+ \(\frac{1}{3^2}\)+....+\(\frac{1}{2014^2}\)+\(\frac{1}{2015^2}\)

chứng toe A<1

giúp mk nhé, mình đang cần gấp
trả lời chi tiết cho mk nhé mk tick cho

Answer 1

 \(\frac{1}{2^2}>\frac{1}{1.2}=1-\frac{1}{2}\)

\(\frac{1}{3^2}>\frac{1}{2.3}=\frac{1}{2}-\frac{1}{3}\)

\(....\)

\(\frac{1}{2015^2}>\frac{1}{2014.2015}=\frac{1}{2014}-\frac{1}{2015}\)

nên \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2015^2}>1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2004}-\frac{1}{2005}\)

\(=1-\frac{1}{2005}\)

vì \(1-\frac{1}{2005}< 1\)

=> ĐPCM