Question

so sánh:\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+....+\frac{1}{100^2}\) với \(\frac{2}{3}\)

Answer 1

122 =14 

          132 <12.3 

            .............

           11002 <199.100 

⇒A<14 +12.3 +....+199.100 

⇒A<14 +12 −13 +...+199 −1100 

⇒A<14 +12 −1100 

⇒A<14 <34 

Answer 2

\(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\)

\(A>\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{100\cdot101}\)

\(A>\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{100}-\frac{1}{101}\)

\(A>\frac{1}{2}-\frac{1}{101}=\frac{99}{202}>\frac{2}{3}\)

\(\Rightarrow A>\frac{2}{3}\)

Answer 3

giúp mk vs