Question

Chứng tỏ rằng:

\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}< 1\)

Answer 1

Ta có : \(\frac{1}{2^2}< \frac{1}{1.2}\)

\(\frac{1}{3^2}< \frac{1}{2.3}\)

....

\(\frac{1}{10^2}\)< \(\frac{1}{9.10}\)

=> \(\frac{1}{2^2}+....+\frac{1}{10^2}\)< \(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{9.10}\)

=> \(\frac{1}{2^2}+....+\frac{1}{10^2}\)< \(\frac{9}{10}\)< 1

=> \(\frac{1}{2^2}+....+\frac{1}{10^2}\)< 1 ( dpcm )

Answer 2

\(\frac{1}{4}\)+\(\frac{1}{9}\)+