Question

Chứng minh :\(1+\frac{1}{2}+\frac{1}{3}+........+\frac{1}{63}+\frac{1}{64}>4\)

Answer 1

làm sao để viets phân số

Answer 2

Các bạn xem mình giải có đúng không:

  \(1+\frac{1}{2}+........+\frac{1}{63}+\frac{1}{64}\)

\(=1+\frac{1}{2}+\left(\frac{1}{3}+\frac{1}{4}\right)+\left(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}\right)+...........+\)\(\left(\frac{1}{33}+\frac{1}{34}+...........+\frac{1}{64}\right)\)

\(>1+\frac{1}{2}+\left(\frac{1}{4}+\frac{1}{4}\right)+\left(\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}\right)+...........+\left(\frac{1}{64}+.....+\frac{1}{64}\right)\)

=\(1+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\)

=4

Vậy \(1+\frac{1}{2}+..............+\frac{1}{64}>4\)