Hello, TreeMoney!

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.

False

The Harmonic Series: does not converge

but its termdoesapproach 0: .

b) If the nth term of a series does not approach 0 as n approaches infinity,

then the series diverges.

True

A necessary condition for convergence is: .

c) If all partial sums of a series are less than some constant L,

then the series converges.

False

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 . . .