I have a couple of Q's I'm stuck on help and help would be MUCH appreciated! I have to use either the limit comparison or the comparison test only -
Sum (n=1 to infinity) n/(2^n)
Sum (n=1 to infinity) 1/(2 + n^0.5)
Consider:
Now I assume that you know that , for , because .
Thus, there exists an , such that , for all , and thus the tail of your first series can be compared with the tail of the geometric serie .
As to your second series my guess is that for sufficiently large , we will have that , thus you can compare it with the divergent harmonic series.
To check whether holds true for sufficiently large , you just note that , if .