I am currently studying computer science (first year) and one of our first courses is Real Analysis. What I'm struggling with the most are all those kinds of "tricks" that you supposedly should be aware of. I'll give an example: $$\sum_{n=1}^\infty \ \frac{1}{4n^2-1}$$
Finding out that this series converges with the comparison test is fairly understandable, but we had to find the sum too. How am I supposed to know that I could get a telescoping sum with partial fraction decomposition?
I know doing a lot of exercises will sharpen my intuition, but the problem is that it already takes so much time to do just two or three of these exercises (a couple of hours). It seems to me like I am missing basic mathematical tools (like partial fraction decomposition) or a better understanding of algebra. Most of my collegues struggle with similar problems. Do you know any good resources, books or exercises that specifically train all those "tools"?
2026-03-28 22:24:49.1774736689
Mathematical tricks for Real Analysis
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