Question

Proof 13.2: Let $s(n, k)$ denote the signless Stirling numbers of the first kind. Using the recursive formula $s(n, k) = s(n - 1, k - 1) + (n - 1)s(n - 1, k)$, prove that $s(n, 2) = (n - 1)! \left(1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n - 1} \right)$.

          Proof 13.2: Let $s(n, k)$ denote the signless Stirling numbers of the first kind. Using the recursive formula $s(n, k) = s(n - 1, k - 1) + (n - 1)s(n - 1, k)$, prove that
$s(n, 2) = (n - 1)! \left(1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n - 1} \right)$.

Proof 13.2: Let s(n, k) denote the signless Stirling numbers of the first kind. Using the recursive formula s(n, k) = s(n - 1, k - 1) + (n - 1)s(n - 1, k), prove that
s(n, 2) = (n - 1)! (1 + (1)/(2) + (1)/(3) + … + (1)/(n - 1)).

Added by Brittany S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/01/2023

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Proof 13.2: Let s(n,k) denote the signless Stirling numbers of the first kind. Using the recursive formulat s(n,k) = s(n-1, k-1) + (n-1)s(n-1, k), prove that s(n, 2) = (n-1)! (1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n-1}).