If $X$ is a Bernoulli random variable with parameter $p$, the probability mass function is given by
$$ f(k) = p^k(1-p)^{1-k} $$
and the loglikelihood, $\ell(p)$, is given by
$$ \ell(p) = \log(p)\sum \limits_{i=1}^n k_i + \log(1-p)\left(n-\sum_{i=1}^nk_i\right). $$
Taking the first derivative with respect to $p$ we get the score function $s(p)$
$$ s(p) = \frac{1}{p} \sum_{i=1}^n k _i - \frac{1}{1-p}\left(n - \sum_{i=1}^n k_i \right) $$
setting this to 0 and solving it for $p$, we get $\hat{p}_{ml}$
$$ \hat{p}_{ml} = \frac{1}{n}\sum_{i=1}^nk_i. $$
I keep having problems to find the Fisher information, which is the negative second derivate of $s(p)$ and according to wikipedia should be:
$$ F(p) = \frac{1}{p(1-p)} $$