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A sequence $d_1, d_2, d_3...$ is defined by letting $d_1=2$ and $d_k=\large\frac{d_{k-1}}{k}$ for all natural numbers $k \geq 2$. Show that $d_n = \large\frac{2}{n!}$ for all $n \in N$ by using principle of mathematical induction.

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