The Ramanujan Essays

The Ramanujan Summation: 1 + 2 + 3 + ⋯ + ∞ = -1/12?

“What on earth are you talking about? There’s no way that’s true!” — My mom

This is what my mom said to me when I told her about this little mathematical anomaly. And it is just that, an anomaly. After all, it defies basic logic. How could adding positive numbers equal not only a negative, but a negative fraction? What the frac?

Before I begin: It has been pointed out to me that when I talk about sum’s in this article, it is not in the traditional sense of…