Problem finding the limit of the remainder of a series
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
The denominator of integrand is greater than or equal to 1;hence
if , the right side of this inequality approaches zero as
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?