liman = 0 , lim b = -1 and lim c = 0
very easy to ustify.....
There is some confusion, your title reads series but your post reads sequences... i'm going to assume you want series behavior.
a)Convergent. It is an alternating series, as
b) Divergent as , its like adding -1 infinite times
c) divergent but a bit harder to show, multiply numerator and denominator by the conjugate. consider the following...
Now compare this with which diverges because the exponent on n is less than 1
for n > 0 so a_n diverges because every nth term of a_n is LARGER than every corresponding nth term of b_n