Consider the following two sequences $<a_n>$ and $<b_n>$ given by $a_n = \frac1{(n+1)} + \frac1{(n+2)} + \frac1{(n+3)} + ......\frac1{(2n)}$ and $b_n= \frac1n$. Which of the following statements is true?
(a) $<a_n>$ converges to $\log 2$ and has the same convergence rate as the sequence $<b_n>$.
(b) $<a_n>$ converges to $\log 4$, and has the same convergence rate as the sequence $<b_n>$.
(c) $<a_n>$ converges to $\log 2$ but does not have the same convergence rate as the sequence $<b_n>$.
(d) $<a_n>$ does not converges.
My attempt:- as $<a_n>$ is integral sum thus $\lim <a_n>$ converges to log 2.
I am confused about how to show $<a_n>$ has the same convergence rate as $<b_n>$. If not, then How?