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Hi there and welcome to my blog! This is my first post, with hopefully many to follow.   In my undergraduate years, I learned about a very curious summation discovered by the great Ramanujan. Since then, whenever a student tells me that they hate mathematics and that it is stupid, I show this to them and they almost always see math in a new and enthusiastic light. Here, I will explain the series to you, and hope that it brings you as much excitement and curiousity as it first brought me.   Consider the series 1+2+3+4+5+6+... The series is simple, we simply add two to one, then add three, then four, then 5, and keep going forever. The series is called a "monotonic series", meaning that it is ever increasing. This should be intuitive, since if we look at the first few terms, we have   1 = 1 1 + 2 = 3 1 + 2 + 3 = 6 1 + 2 + 3 + 4 = 10   If we continue the process, this... read more

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