Question

Chứng minh rằng 1-1/2^2-1/3^2-1/4^2-...-1/2009^2>1/2009

ai làm giúp mình với  mình dang cần gấp

Answer 1

\(1-\frac{1}{2^2}-\frac{1}{3^2}-\frac{1}{4^2}-...-\frac{1}{2009^2}\)

\(=1-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2009^2}\right)\)

\(>1-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2008.2009}\right)\)

\(=1-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2008}-\frac{1}{2009}\right)\)

\(=1-\left(1-\frac{1}{2009}\right)\)

\(=\frac{1}{2009}\)