# Log of the likelihood (without the constant)
log.likelihood <- function(pi,successes,n.trials) {
  successes * log(pi) + (n.trials - successes) * log(1-pi)
}

successes <- 21
n.trials <- 50

mle.via.optimize <- optimize(log.likelihood,c(0,1),successes,n.trials,maximum=TRUE)
mle.via.optimize

mle.via.analyticals <- successes/n.trials
mle.via.analyticals