Sarah and Sequences and Series

When we were doing the lab on iteration, there was a proof that we encountered that had heavy use of some of the theorems involving infinite series. While there was a chapter on this in my Calculus II class, I think it would be interesting to explore more about series in the context of a more proof-based class. I think this will also be a nice addendum to the first lab on iteration, because we are going to be looking in much more detail into the question of general convergence and divergence. It doesn’t look like we’re going to be doing a lot of strict proving in this lab, but instead we are gong to given the opportunity to explore series in more detail and really be able to explore some of the facets that may have been glossed over in a busy Calculus class. We will be exploring convergence, divergence, the harmonic series, the natural logarithm and Euler’s constant. I’ve never encountered Euler’s constant outside of some proofs that I saw in other labs.