(a) Define the nth triangular number tn. Give an airtight definition that is mathematically precise.

(b) Find a closed-form formula for tn and prove by induction that your formula is correct. To receive credit for this problem, show all of your work, reasoning, and justification, write complete sentences, and do not leave out any details. Correct syntax and set of complete steps for an induction proof must be followed. For example writing P(n) = will result in a loss of points since P(n) is a statement and not an equation.