Q) prove that –
…..



My bashed up solution :
let be …..

Note that :




………



This is because –



Or, .


Hence we have,




…..


Also, we have –




and so on

So we have



For the other inequality, we use a similar approach –



That means, .

n can take values from to .

So we must have




….




So we have .

Official solution : use am – hm for part.

And for the other part,

Grouping together terms at a time,