Hi everyone,

I need to determine whether the sequence

, where

, is decreasing or increasing. To do that, I can first suppose that it's e.g. increasing, and then see if the relation

holds for every

. In other words, if the inequality

*is* true, then is also

, and if it

*isn't*, then

and the sequence is decreasing. This is where I got stuck, for no matter how I tried to solve this inequality (squaring both sides; multiplying whole inequality by both denominators etc), I can't seem to arrive at the solution.

To give you a better idea of the way I am supposed to solve this, here is an easier example:

determine whether the sequence

, where

, is decreasing or increasing.

We can start by assuming that

is increasing; in that case

is true if and only if

, which

*is* true, and therefore the starting assumption (

) is also true, and

is an increasing sequence.

So, basically, I should somehow arrive from this expression:

to a statement from which the verity of the starting assumption (i.e.

) could be inferred.

Many thanks.