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Sum 1/(1! (n-1)!) + 1/(3! (n-3)!) + ... of odd-even factorial pairs

The same question, asked 2 times: 1 Feb 2023*, 24 Jan 2026 S1. Every wording below, oldest first.

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  1. Question 1

    1 Feb 2023

    69
    The value of 11!50!+13!48!+15!46!+⋯ .+149!2!+151!1!\frac{1}{1!50!}+\frac{1}{3!48!}+\frac{1}{5!46!}+ \cdots. +\frac{1}{49!2!}+\frac{1}{51!1!} is:

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  2. Question 2

    24 Jan 2026 S1

    64
    Let S=125!+13!23!+15!21!+…S =\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+ \ldots up to 13 terms. if 13 S=2kn!,k∈N13\text{ }S =\frac{2^{k}}{n!},k \in N, then n+kn + k is equal to

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