Short solutions of the suggested list of exercises

1) a) The value is $\infty$ since the series is monotonic increasing and unbounded,
b) The value is 1,
c) The value is 2.

2) i) Divergent, Comparison Test by $1/2n$,
ii) Convergent iff $s>1$,
iii) Convergent, Integral Test,
iv) Convergent, Limit Comparison with $1/n^{5/2}$,
v) Convergent, Root Test,
vi) Convergent, Ratio Test,
vii) Convergent, Root Test,
viii) Divergent, n-th Term Test,
ix) Divergent, n-th Term Test,
x) Convergent, Ratio Test,
xi) Divergent, Ratio Test.

P.S: You need to provide more detailed explanations in the exam.