A sequence x1,x2,x3,...... is defined by letting x1=2 and xk=xk−1n f – InterviewSolution

1.	A sequence x1,x2,x3,...... is defined by letting x1=2 and xk=xk−1n for all natural numbers k, k≥2. Show that xn=2n! for all nϵN.
Answer» A sequence $x_{1}, x_{2}, x_{3}, . . . . . .$ is defined by letting $x_{1} = 2$ and $x_{k} = \frac{x_{k - 1}}{n}$ for all natural numbers k, $k \geq 2$ . Show that $x_{n} = \frac{2}{n!}$ for all $n ϵ N$ .

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