While revising for my probability test, I saw this question from one of the previous exams:

You flip a fair coin 100 times. What is the probability that you have less than 45 heads?

My question is a simple one. I know that to calculate the probability of a specific amount of n heads (or tails), we can use the binomial distribution with formula $P(X=k)={\textstyle (}\genfrac{}{}{0ex}{}{n}{k}{\textstyle )}{p}^{k}(1-p{)}^{n-k}$, with $n=100$ and $p=0.5$ in this case. I also know that we can compute the chance of $P(X<k)$ as either $P(X=0)+P(X=1)+...+P(X=k-10)$ or $1-(P(X=k)+P(X=k+1)+...+P(X=n))$

However this is a simple question only worth two points out of over 60 total points. I cannot imagine that you need to compute $P(X=n)$ 44 separate times and sum them together for such a small amount of points.

Is there any way to rewrite the formula or apply a different trick to drastically lower the amount of computations you need to do?