Question: Question 3 The first five triangular numbers are shown, where n represents the number of dots in the base of the figure, andd(n) represents the

Question 3

The first five triangular numbers are shown, wherenrepresents the number of dots in the base of the figure, andd(n)

represents the total number of dots in the figure.

Whenn=1

, there is 1 dot.Whenn=2

, there are 3 dots.Whenn=3

, there are 6 dots.Notice that the total number of dotsd(n)

increases byneach time.

Use induction to prove thatd(n)=n(n+1)2

.

Part A

Prove the statement is true forn=1

.

Type your answer in the box.

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