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MIT Integration Bee 2023 – Finals Problem 5

Are we doing okay so far? Let’s move on to the last problem of the competition, an absolute cracker of a problem: \displaystyle I = \int_0^1 \left( \sum_{n=1}^{\infty} \frac{ \lfloor 2^n x \rfloor }{3^n} \right)^2 \: \mathrm{d}x . This problem, I have no shame in admitting, had me stumped. In this post, I will…

MIT Integration Bee 2023 – Finals Problem 4

Problem 4 of the bee asks us to find the value of \displaystyle C = \Bigg\lfloor 10^{20} \int_2^{\infty} \frac{x^9}{x^{20} – 48x^{10} + 575} \: \mathrm{d}x \Bigg\rfloor . In many ways, this was the simplest problem of the bee, with only the floor function proving to induce a bit of complexity but also making it…

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