Hi guys,
please can someone here help me to prove that:
Assume that:
this implies that:
thanks in advance
Then it is simple.
Otherwise the expression is undefined.
Now, if is decreasing function and continous then,
is decreasing.
And we are told that,
Converges.
That means, by the integral test,
Converges.
But that means that,
.
Thus,
We now that,
*)
This is a L'Hopital rule problem.
(But then we need to know that the function is differenciable).
*)I am not sure about this. Perhaps this statement works only the other way.