Suppose there is a series
in which the last term comes from adding the remaining terms as a
geometric series with the first term
and ratio
Integrating both sides of equation from
to
gives
where
The denominator of integrand is greater than or equal to 1;hence
if
, the right side of this inequality approaches zero as
Therefore
Now my question is how the book found the limit of
as 0?
Book showed and I understand that the limit of
is 0 when n
approaches
. But that's only half of it? The author did not calculate
the limit of integral
as a whole. I don't understand how he
reached the conclusion? Obviously I'm missing something simple. Is
there any theorem that i'm unaware of? Anyone knows how
he reached the conclusion?