is the series (n=1 to infinity) for:
-1/(x+1)
divergent or convergent, and how do you prove it?

Question

is the series (n=1 to infinity) for:   
-1/(x+1)
divergent or convergent, and how do you prove it?

anonymous · Answer

is it (-1)^{n}/(x+1) ? otherwise the answer would be -1/(x+1) since the function or sequence you are looking at does not depend on n.

anonymous · Answer

$$(-1)^{n}/(x+1)$$

anonymous · Answer

Sorry, I meant for -[(1)/(n+1)], I shouldn't have included x.  Since this is in general harmonic form, can I say it is divergent? Thanks.

anonymous · Answer

yes. look at limit comparison test

anonymous · Answer

actually, if you look at the sequence, if the entire thing is negative, then you can just do comparison test to harmonic series. just take absolute value of your sequence first

anonymous · Answer

That makes sense, thanks a bunch :D