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A sequence d1 , d2 , d3 ... is defined by letting d1 = 2 and dk = dk−1/k for all natural numbers, k ≥ 2. Show that dn = 2/n! for all n ∈ N.

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A sequence d1 , d2 , d3 ... is defined by letting d1 = 2 and dk = dk−1/k for all natural numbers, k ≥ 2. Show that dn = 2/n! for all n ∈ N.

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Given; A sequence d1, d2, d3 …. Is defined by letting d1 = 2 and dk = dk - 1/k.

⇒ dm+1 is true when dm is true.

∴ By Mathematical Induction dn = 2/n! is true for all natural numbers n.

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