Question

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

Answer 1

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.

Answer 2

\[(-1)^{n}/(x+1)\]

Answer 3

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.

Answer 4

yes. look at limit comparison test

Answer 5

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

Answer 6

That makes sense, thanks a bunch :D