I have been studying binomial theorem and have been practicing the methods to find the results of summations involving binomial coefficients and in one of the books I own, I came across this limit of a summation involving binomial coefficients:
$$\lim_{n\to\infty}\sum_{r=0}^n(-1)^r\binom{n}{2r}\left(\frac{x}{n}\right)^{2r}$$
I have tried almost all the methods I have learnt which are to be used in order to find such sums, but this one has completely stumped me. Any kind of hints/solutions/explanations would be highly appreciated.