Question

[trần nhật khánh đoan]

CHO A= \(\frac{3^2}{4}\)+\(\frac{3^2}{28}\)+\(\frac{3^2}{70}\)+\(\frac{3^2}{120}\)+...+\(\frac{3^2}{3190}\). SO SÁNH A VÀ \(\frac{10}{3}\)

 PLEASE HELP NHA (GHI GIÚP MIK CÁCH LÀM LUÔN NHA) MƠN NHIUD NHÌU!!!!!!!!!!!

Answer 1

[zZz Cool Kid_new zZz]

\(A=3\left(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+.....+\frac{3}{55\cdot58}\right)\)

\(A=3\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+.....+\frac{1}{55}-\frac{1}{58}\right)\)

\(A=3\left(1-\frac{1}{58}\right)\)

\(A=3-\frac{1}{174}< 3< \frac{10}{3}\)