Let $S=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+\ldots$ up to 13 terms. If $13S=\frac{{2}^{k}}{n!},k\in ℕ,$ then $n + k$ is equal to [JEE Main 2026, 24 Jan (Shift 1)]

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Let \(S=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+\ldots\) up to 13 terms. If \(13S=\frac{{2}^{k}}{n!},k\in ℕ,\) the…

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