A Family of Infinite Series (Solved)

Summary: Let $S_N := \sum_{k=0}^{\infty} (k/e)^k/(k+N)!$. Prove that $S_N = P_N(e)$, where $P_N$ is a rational polynomial in $e$ of degree $N$, and determine the coefficients of $P_N$.

Classification: Primary, classical analysis; Secondary, sequences and series

• Download Problem [PDF]
  
  Jonathan Borwein
  CECM
  Department of Mathematics and Statistics
  Simon Fraser University
  Burnaby, BC, V5A 1S6
  Canada
  e-mail: [email protected]
  
  
• Download Solution: "All in the Family" [PDF]
  
  David Borwein
  Department of Mathematics and Statistics
  University of Western Ontario
  London, ON, N6A 5B7
  Canada
  
  
• Download Solution: "An Eulerian Approach" [PDF]
  
  Vinicius-Nicolae-Petre Anghel
  AECL Chalk River Laboratory (Stn. 91)
  Plant Road
  Chalk River, Ontario K0J 1P0
  Canada
  e-mail: [email protected]
  
  
• Download Solution: "How the Discovery Was Made" [PDF]
  
  Jonathan Borwein
  CECM
  Department of Mathematics and Statistics
  Simon Fraser University
  Burnaby, BC, V5A 1S6
  Canada
  e-mail: [email protected]

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