Proof of the probability distribution of a binomial and geometric random variables is indeed a valid probability function

Question

How can I proof this two theorem?

Exercise 3.^src) Show that the probability distribution of a binomial random variable $X$ is indeed a valid probability function. That is, show that $$ \sum_{j=0}^{n}\operatorname{Pr}(X = j) = 1. $$

Exercise 6.^src) Show that the probability distribution of a geometric random variable $X$ is indeed a valid probability function. That is, show that $$ \sum_{j\geq 1}\operatorname{Pr}(X = j) = 1. $$

For the binomial random variable the teacher give us a tip that says: "Use the Binomial Theorem or prove by induction"