My professor has posted a sample midterm on her web site, but although she promised to post the solutions as well, she hasn't yet and I don't really expect her to at this point since the midterm is tomorrow. I have a few questions about some of the problems on the midterm. The sample exam can be found here: http://www.math.psu.edu/li/math312/hw.html(adsbygoogle = window.adsbygoogle || []).push({});

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 problems6-8, 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.

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# Real Analysis - Sample Midterm Help

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