Statistics with series and probability with infinitesimals

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community. My name is Henry, and I enjoy mathematics. This is my first question. I have a good understanding of Algebra, and a general understanding of many things that go with it. However, in regard to statistics as well as probability (the more challenging stuff) I am lost, and a bit discouraged because I wish for this to me a strong suit of mine. If anybody would be willing, can you give me a general understanding for infinite series and their relation to probability and statistics, as well as the different infinitesimal series. For example, things like eulers number I understand, and have even memorized some of the digits. However, it's relation to log odds and other odds? It would be useful to know this, as well as many other things in this area involving the same thinking process. Thanks!