{
  "id": "2106.03659",
  "version": "v1",
  "published": "2021-06-04T16:25:35.000Z",
  "updated": "2021-06-04T16:25:35.000Z",
  "title": "Partial Sums of the Fibonacci Sequence",
  "authors": [
    "Hung Viet Chu"
  ],
  "comment": "4 pages",
  "journal": "Fib. Quart., 59:2 (May 2021), 132-135",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Let $(F_n)_{n\\ge 1}$ be the Fibonacci sequence. Define $P(F_n): = (\\sum_{i=1}^n F_i)_{n\\ge 1}$; that is, the function $P$ gives the sequence of partial sums of $(F_n)$. In this paper, we first give an identity involving $P^k(F_n)$, which is the resulting sequence from applying $P$ to $(F_n)$ $k$ times. Second, we provide a combinatorial interpretation of the numbers in $P^k(F_n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-04T16:25:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39"
    ],
    "keywords": [
      "fibonacci sequence",
      "partial sums",
      "combinatorial interpretation",
      "resulting sequence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}