IIT JEE , AIEEE Forum - Mathematics , Algebra

konichiwa2x

Here is another way of proving it.

If

, then to prove the inequality

it seems natural to guess that

It should be easy enough to prove that by induction.

The other inequality,

, looks harder. One approach would be to write

. Then you can use the inequality

. That would give

Hence you can go on to show that

Edit: a better approach is to notice that ?(1998)=44.69... . That suggests the inequality

another straightforward induction proof