For each general term, determine whether the sequence converges or diverges. If it converges, find the value.

$($a$)a_n=\frac{2n1}{5n-2}$

$($b$)a_n=(-1{)}^n\frac{n-1}{2n}$

$($c$)a_n=\frac{2^n-1}{n}$

Find an expression for $a_n$ and determine whether each sequence converges or diverges. If it converges, find the value.

$($a$)\{1,\frac{4}{3},\frac{9}{7},\frac{16}{15},\frac{25}{31},$dots$\},a_n=$

$($b$)\{\frac{2}{3},\frac{5}{6},\frac{10}{9},\frac{17}{12},\frac{26}{15},$dots$\},a_n=$For each telescoping series, find its sum.

$($a$){\displaystyle \underset{n=1}{\overset{}{}}}ln(\frac{n1}{n})$

$($b$){\displaystyle \underset{n=1}{\overset{}{}}}\frac{2}{n^{2}2n}$