An algebra problem by krishna mandalika

Algebra Level 3

From 2 n + 1 2n + 1 consecutive positive integers, 3 are selected at random without replacement.

What is the probability that they are in an arithmetic progression ?

3 n 4 n 2 + 1 \dfrac{3n}{4n^{2} +1} 3 4 n \dfrac{3}{4n} n 2 4 n 2 1 \dfrac{n^{2}}{4n^{2} - 1} 3 n 4 n 2 1 \dfrac{3n}{4n^{2} - 1}

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