Question

chứng tỏ 1/3^2 + 1/4^2+1/5^2+...+1/100<1/2

1/100 #^2=10^2

nhanh và đúng me sẽ chọn!

Answer 1

Ta thấy: \(\dfrac{1}{3^2}< \dfrac{1}{2.3}\)

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

\(...\)

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

\(\Rightarrow\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}< \dfrac{1}{2.3}+...+\dfrac{1}{99.100}\)

\(\Rightarrow\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}< \dfrac{1}{2}-\dfrac{1}{100}\)

\(\Rightarrow\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}< \dfrac{49}{100}< \dfrac{50}{100}< \dfrac{1}{2}\) (ĐPCM)