The first five triangular numbers are shown, where n represents the number of dots in the base of the figure, and d(n) represents the total number of dots in the figure.

When n = 1, there is 1 dot. When n = 2, there are 3 dots. When n = 3, there are 6 dots. Notice that the total
number of dots d(n) increases by n each time.

Use induction to prove that
d (n) = n(n+1)/2

Part A:
Prove the statement is true for n = 1.

Part B:
Assume the statement is true for n=k. Prove that it must be true for n=k+1, therefore proving it true for all natural numbers, n.

hint: since the total number of dots increases by n each time, prove that d(k)+(k+1)=d(k+1)