A sequence `x_1, x_2, x_3,....` is defined by letting `x_1=2` and `x_k=x_(k-1)/k` for all natural numbers `k,k>=2` Show that `x_n=2/(n!)` for all `n in N`.

Explanation

A sequence `x_1, x_2, x_3, ….` is defined by letting x_1 = 2 and `x_k = (X_(k−1))/ n` for all natural number k,k ≥ 2


let `p(n)=(X_(k−1))/ n
p(1)=2/1=2`

so,it is true for n=1

Now, we need to show P(k+1) is true whenever P(k) is true. P(k+1)

`x_(k+1) = (X_(k))/ (k)`

`=2/((k)xxk!)`

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