\[\Large {\lim_{n \to \infty}} {\dfrac{\displaystyle{\large\displaystyle \sum^{n}_{k=0}\dbinom{n}{k}}}{\large\displaystyle \sum^{n/m}_{k=0}\dbinom{n}{mk}}}\]

If \(n\) is a multiple of some positive integer \(m\), find the limit above.

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