Determine whether the following infinite series are convergent or divergent

i) $\displaystyle \sum_{n=1}^{\infty }{\frac{n}{n+1}}$

ii)$\displaystyle \sum_{n=1}^{\infty }{\frac{n \sqrt{n}}{n^2+1}}$

iii)$\displaystyle \sum_{n=2}^{\infty }{\frac{1}{n^2-1}}$

for part 1 and 2 i tired doing ratio test and integral test but they both failed and i got nowhere. anyone want to give me a hand ?

part 3 seems a lot easier it seems to converge to 0.75 which is easily proved using partial fractions