- #1

steelphantom

- 159

- 0

**2(c):**[tex]\sum[/tex] (2 / (3 - (-1)

^{n}))

^{n}

This series diverges, but how would I go about proving it? The first thing I thought of was the root test, but the limit of the series does not exist. What other way could I try to do this?

**3:**Consider a nonnegative series [tex]\sum[/tex]a

_{n}. If there exists an M such that A

_{N}= [tex]\sum_{n=1}^N[/tex]a

_{n}<= M for all N, then [tex]\sum[/tex]a

_{n}is convergent.

This doesn't say to explicitly prove this, but I assume that's what I need to do. Isn't this true from the definition of convergence of infinite series?

For problems

**6-8**, it says "Find the limit of xxx." I can just stare at them and figure out what the limit is, but that's obviously not what my professor wants me to do. I guess the only thing I could do is say what the limit is and then prove it using the definition of a limit.

I know I should have asked my prof personally about this stuff, but I couldn't make her office hours yesterday, and the next office hours are Thursday, which will do me no good. As always, thanks for any help.