Is it possible for a series to converge without the constraint that a(sub.n+1)< or equal to a(sub.n)? Can we have a convergent series with only the requirement a(sub.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 conjecture stated, the math that shows these series diverge, how you came up with your 3 series and what makes your series diverge
If no include the series to prove your conjecture, the math that shows your series converges, how you made your series and what makes your series converge