Question

Answer 1

Giải:

Gọi biểu thức là A, ta có:

\(A=\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{36}+\dfrac{1}{64}+\dfrac{1}{100}+\dfrac{1}{144}+\dfrac{1}{196}+\dfrac{1}{256}+\dfrac{1}{324}\) 

\(A=\dfrac{1}{2^2}+\dfrac{1}{4^2}+\dfrac{1}{6^2}+\dfrac{1}{8^2}+\dfrac{1}{10^2}+\dfrac{1}{12^2}+\dfrac{1}{14^2}+\dfrac{1}{16^2}+\dfrac{1}{18^2}\) 

\(A=\dfrac{1}{2^2}.\left(1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+\dfrac{1}{8^2}+\dfrac{1}{9^2}\right)\) 

\(\Rightarrow A< \dfrac{1}{2^2}.\left(1+1\right)=\dfrac{1}{4}.2=\dfrac{1}{2}\) 

\(\Rightarrow A< \dfrac{1}{2}\left(đpcm\right)\) 

Chúc bạn học tốt!