Question

So sánh tổng A với 5/12:

A = 1/4 + 1/9 +1/16 + ... + 1/100 + 1/121

GIÚP MÌNH NHA !

Answer 1

\(A=\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{100}+\frac{1}{121}\)

    \(=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}+\frac{1}{11^2}\)

Ta có:  \(\frac{1}{2^2}>\frac{1}{2}-\frac{1}{3}\)

           \(\frac{1}{3^2}>\frac{1}{3}-\frac{1}{4}\)

            \(\frac{1}{4^2}>\frac{1}{4}-\frac{1}{5}\)

             ................................

            \(\frac{1}{10^2}>\frac{1}{10}-\frac{1}{11}\)

            \(\frac{1}{11^2}>\frac{1}{11}-\frac{1}{12}\)

Cộng theo vế ta được:

                  \(A>\frac{1}{2}-\frac{1}{12}=\frac{5}{12}\)

Vậy  \(A>\frac{5}{12}\)