Question

So sánh C= 1/2^2 + 1/3^2+1/4^2+...+1/2022^2 với 13/18

Answer 1

\(C=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{2022^2}\)

\(C=\dfrac{1}{\left(2+3+4+...+2022\right)^2}\)

\(C=\dfrac{1}{\left(2022-2+1\right)^2}\)

\(C=\dfrac{1}{2021^2}\)

\(C=\dfrac{1}{2021\cdot2021}\)

\(C=\dfrac{1\div2021}{2021}\)

\(C=1\)

Vì \(1>\dfrac{13}{18}\)

\(\Rightarrow C>\dfrac{13}{18}\)