Which statement is correct about the European option prices estimated from the binomial model and Black-Scholes-Merton (BSM) model (assume same exercise price, expiration time, and underlying stock)?

As the number of periods in a binomial situation approaches infinity, the difference of the option prices estimated from the binomial model and BSM model will get larger.

The option prices calculated from the binomial model can never be same as those calculated from the BSM model.

As the number of periods in a binomial model situation approaches infinity, the option prices estimated from the binomial model will approach (nearly equal to) those estimated from the BSM model.

Since binomial model assumes only two outcomes in each period, there should not be any relation between the option prices estimated from the binomial and BS models regardless of the number of periods in a given time to expiration.