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Omni-MATH / Let ABC be a triangle in the plane with AB=13,BC=14,AC=15. Let M_(n) denote the smallest possible value of (AP^(n)+BP^(n)+CP^(n))^((1)/(n)) over all points P in the plane. Find …

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problem

Let ABCABC be a triangle in the plane with AB=13,BC=14,AC=15AB=13, BC=14, AC=15. Let MnM_{n} denote the smallest possible value of (APn+BPn+CPn)1n\left(AP^{n}+BP^{n}+CP^{n}\right)^{\frac{1}{n}} over all points PP in the plane. Find limn→∞Mn\lim _{n \rightarrow \infty} M_{n}.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle in the plane with AB=13,BC=14,AC=15. Let M_(n) denote the smallest possible value of (AP^(n)+BP^(n)+CP^(n))^((1)/(n)) over all points P in the plane. Find lim_(n→∞)M_(n).
Original LaTeX notation
Let $ABC$ be a triangle in the plane with $AB=13, BC=14, AC=15$. Let $M_{n}$ denote the smallest possible value of $\left(AP^{n}+BP^{n}+CP^{n}\right)^{\frac{1}{n}}$ over all points $P$ in the plane. Find $\lim _{n \rightarrow \infty} M_{n}$.

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task_id
f64885d3-f08c-51b8-9136-472d0e91b880
task_key
test--f64885d3-f08c-51b8-9136-472d0e91b880
task_revision_id
1
config / split
/ test

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