Chapter 5.7, Problem 1ES

The formula $1+2+3+\cdot \cdot \cdot +n=\frac{n\left(n+1\right)}{2}$ is true for every integer $n\ge 1.$ Use this fact to solve each of the following problems.
a. If k is an integer and $k\ge 2,$ find a formula for the expression $1+2+3+\cdot \cdot \cdot +\left(k-1\right).$
b. If n is an integer and $n\ge 1,$ find a formula for the expression $5+2+4+6+8+\cdot \cdot \cdot +2n.$
c. If n is an integer and $n\ge 1,$ find a formula for the expression $3+3\cdot 2+3\cdot 3+\cdot \cdot \cdot +3\cdot n+n.$