Question

[trucdao giaovien]

Chung minh1/3^2+1/4^2+1/5^2+..........+1/100^2<1/2

Lam on giai ki giup minh. Minh can trong 30 phut nua

Answer 1

[Thao Nhi]

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

\(\frac{1}{4^2}<\frac{1}{3.4}\)

...

\(\frac{1}{100^2}<\frac{1}{99.100}\)

===>\(\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}<\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}<\frac{50}{100}=\frac{1}{2}\)