2.10.114 Number Series

Condition: investigate the ranks for the convergence: 1) \ (\ sum_ {n = 1}^{\ infty} \ left (\ frac {9 n^{2} +1} {2 n^{2} +5} \ risht) {n} \), 2) \ (( \ sum_ {n = 1}^{\ infty} \ frac {(-1)^{n} n} {n \ sqrt {n} -1} \), 3) \ (\ sum_ {n = 1}^{\ infty} {n} \ sin \ sin \ frac {\ pi} {2^{n}} \)