# Convergence and the Alternating Series test

Is it possible for a series to converge without the constraint that a_n+1< or equal to a_n? Can we have a convergent series with only the requirement a_n >0 and the limit as x approaches infinity = 0 (i.e. not a decreasing monotonic series)?

If yes include 3 series which disprove the original conjecture stated, the math that shows these series diverge, how you came up with your 3 series and what makes your series diverge

Is this a homework question? If so, it should be posted in the homework section, and you should show what you have done so far, and people will give you hints or help.