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)

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- Apr 26th 2010, 11:35 AMamywilliams99Convergent/Divergent Series help!
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) - Apr 26th 2010, 11:54 AMFailure
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 .