# Alternating Series Calculus Help!!

Discussion in 'Undergraduate Math' started by Brian, Jan 9, 2011.

1. ### BrianGuest

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

Brian, Jan 9, 2011

2. ### Brian M. ScottGuest

On Sat, 08 Jan 2011 23:06:54 EST, Brian
Yes, it is possible, but this looks too much like a homework
question for me to be willing to go any further.

[...]

Brian

Brian M. Scott, Jan 9, 2011

3. ### VirgilGuest

My take exactly!

But hint:

ANY finite series followed by a convergent series converges.

Virgil, Jan 9, 2011