Devise an algorithm that finds the sum of all integers in a list $a_1,$dots,$a_n$ where $n2.$

Give a recursive algorithm for finding $nx$ whenever $n$ is a is a positive integer and $x$ is an integer, using only addition. $($So$,$ you want to find $n$ times $x,$ when inputting $n$ and $x.)$

Prove your algorithm in #$3$ is correct using induction on $n.$