Question

cmr:1/4²+1/6²+1/8²+...+1/(2n)²<1/4

Answer 1

1/4²+1/6²+1/8²+...+1/(2n)²

=1/2².2²+1/2².3²+1/2².4²+...+1/2².n²

=1/2².(1/2²+1/3²+1/4²+...+1/n²)<1/2².(1/1.2+1/2.3+1/3.4+...+1/(n-1).n)

                                              <1/4.(1-1/2+1/2-1/3+1/3-1/4+...+1/n-1-1/n)

                                              <1/4.(1-1/n)<1/4

Answer 2

1/4²+1/6²+1/8²+...+1/(2n)²

=1/2².2²+1/2².3²+1/2².4²+...+1/2².n²

=1/2².(1/2²+1/3²+1/4²+...+1/n²)<1/2².(1/1.2+1/2.3+1/3.4+...+1/(n-1).n)

                                              <1/4.(1-1/2+1/2-1/3+1/3-1/4+...+1/n-1-1/n)

                                              <1/4.(1-1/n)<1/4