2.10.129 Number Series

Condition: explore the rows to the convergence: 1) \ (\ sum_ {n = 1} ^{\ infty} \ frac {\ cos ^{2} \ left (\ frac {\ pi n} {2} \ right)} {n (n+1) (n+2) \), \), \) 2) \ (\ sum_ {n = 1}^{\ infty} \ ln \ frac {n^{2} +5} {n^{2} +4} \), 3) \ (\ sum_ {n = 1}^\ Infty} \ frac {2^{n+1} \ left (n^{3} +1 \ right)} {(n+1)!} \).