User Tashi - MathOverflow

Tashi

Member for 3 years
Last seen more than 2 years ago

Romania

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I am a high school student. Nowadays mathematical olympiads are my thing. I also love solving KöMaL A problems every month.

My favourite areas of Maths are Geometry, Graph Theory and Mechanics.

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Dec 14, 2021
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Dec 14, 2021
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Dec 14, 2021

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21

Prove that $\lim_{m\to\infty} \sum_{n=0}^{m} \frac{(-1)^n}{n!} \binom{m}{n}=0$.

5

Prove that $ \sum_{k=0}^n \frac{(-1)^k}{k!}\binom{n}{k}=e\int_0^\infty \frac{t^ne^{-t}}{n!} J_0(2\sqrt{t})\;\mathrm{d}t$ using only real analysis.