Here are a few of them . . .
True or False
a) If a series does not converge, then its nth term does not approach 0
as n approaches infinity.
The Harmonic Series: does not converge
but its term does approach 0: .
b) If the nth term of a series does not approach 0 as n approaches infinity,
then the series diverges.
A necessary condition for convergence is: .
c) If all partial sums of a series are less than some constant L,
then the series converges.
The oscillating series: . has a sum less than 2,
. . but it diverges.
d) If a series converges, then there is a constant L
such that all of its partial sums are less than L.
I'll let you think about this one . . .